LMFDB - Embedded newform 336.2.s.d.155.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.15
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.641365 + 1.26042i) q^{2} +(-0.262630 - 1.71202i) q^{3} +(-1.17730 + 1.61678i) q^{4} +(-2.76208 + 2.76208i) q^{5} +(1.98942 - 1.42906i) q^{6} +1.00000 q^{7} +(-2.79289 - 0.446945i) q^{8} +(-2.86205 + 0.899256i) q^{9} +O(q^{10})$	\(q+(0.641365 + 1.26042i) q^{2} +(-0.262630 - 1.71202i) q^{3} +(-1.17730 + 1.61678i) q^{4} +(-2.76208 + 2.76208i) q^{5} +(1.98942 - 1.42906i) q^{6} +1.00000 q^{7} +(-2.79289 - 0.446945i) q^{8} +(-2.86205 + 0.899256i) q^{9} +(-5.25287 - 1.70987i) q^{10} +(-3.92989 - 3.92989i) q^{11} +(3.07715 + 1.59095i) q^{12} +(-1.26876 + 1.26876i) q^{13} +(0.641365 + 1.26042i) q^{14} +(5.45415 + 4.00334i) q^{15} +(-1.22793 - 3.80686i) q^{16} +7.10884i q^{17} +(-2.96906 - 3.03063i) q^{18} +(-0.652997 - 0.652997i) q^{19} +(-1.21386 - 7.71746i) q^{20} +(-0.262630 - 1.71202i) q^{21} +(2.43280 - 7.47379i) q^{22} +3.98276i q^{23} +(-0.0316852 + 4.89888i) q^{24} -10.2582i q^{25} +(-2.41291 - 0.785428i) q^{26} +(2.29121 + 4.66373i) q^{27} +(-1.17730 + 1.61678i) q^{28} +(-0.280064 - 0.280064i) q^{29} +(-1.54778 + 9.44211i) q^{30} +2.51952i q^{31} +(4.01068 - 3.98929i) q^{32} +(-5.69595 + 7.76016i) q^{33} +(-8.96010 + 4.55937i) q^{34} +(-2.76208 + 2.76208i) q^{35} +(1.91560 - 5.68599i) q^{36} +(2.94433 + 2.94433i) q^{37} +(0.404238 - 1.24186i) q^{38} +(2.50536 + 1.83893i) q^{39} +(8.94869 - 6.47969i) q^{40} -5.39610 q^{41} +(1.98942 - 1.42906i) q^{42} +(-1.15575 + 1.15575i) q^{43} +(10.9804 - 1.72709i) q^{44} +(5.42140 - 10.3890i) q^{45} +(-5.01994 + 2.55441i) q^{46} +5.00105 q^{47} +(-6.19495 + 3.10203i) q^{48} +1.00000 q^{49} +(12.9296 - 6.57924i) q^{50} +(12.1705 - 1.86699i) q^{51} +(-0.557588 - 3.54501i) q^{52} +(6.25168 - 6.25168i) q^{53} +(-4.40874 + 5.87903i) q^{54} +21.7093 q^{55} +(-2.79289 - 0.446945i) q^{56} +(-0.946449 + 1.28944i) q^{57} +(0.173374 - 0.532620i) q^{58} +(1.75981 + 1.75981i) q^{59} +(-12.8937 + 4.10500i) q^{60} +(-2.02736 + 2.02736i) q^{61} +(-3.17564 + 1.61593i) q^{62} +(-2.86205 + 0.899256i) q^{63} +(7.60048 + 2.49654i) q^{64} -7.00883i q^{65} +(-13.4342 - 2.20218i) q^{66} +(-0.986955 - 0.986955i) q^{67} +(-11.4934 - 8.36924i) q^{68} +(6.81859 - 1.04599i) q^{69} +(-5.25287 - 1.70987i) q^{70} +5.74760i q^{71} +(8.39532 - 1.23234i) q^{72} +0.913402i q^{73} +(-1.82269 + 5.59948i) q^{74} +(-17.5622 + 2.69410i) q^{75} +(1.82452 - 0.286976i) q^{76} +(-3.92989 - 3.92989i) q^{77} +(-0.710970 + 4.33723i) q^{78} -3.77043i q^{79} +(13.9065 + 7.12323i) q^{80} +(7.38268 - 5.14744i) q^{81} +(-3.46087 - 6.80133i) q^{82} +(-9.11508 + 9.11508i) q^{83} +(3.07715 + 1.59095i) q^{84} +(-19.6352 - 19.6352i) q^{85} +(-2.19799 - 0.715470i) q^{86} +(-0.405923 + 0.553029i) q^{87} +(9.21930 + 12.7322i) q^{88} -2.10538 q^{89} +(16.5716 + 0.170053i) q^{90} +(-1.26876 + 1.26876i) q^{91} +(-6.43923 - 4.68891i) q^{92} +(4.31347 - 0.661699i) q^{93} +(3.20750 + 6.30340i) q^{94} +3.60726 q^{95} +(-7.88308 - 5.81868i) q^{96} +11.0425 q^{97} +(0.641365 + 1.26042i) q^{98} +(14.7815 + 7.71356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) $ 48 * q + 6 * q^6 + 48 * q^7	$ 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) $ 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.641365	+	1.26042i	0.453514	+	0.891249i
$2$	0.641365	+	1.26042i	0.453514	+	0.891249i
$3$	−0.262630	−	1.71202i	−0.151629	−	0.988437i
$3$	−0.262630	−	1.71202i	−0.151629	−	0.988437i
$4$	−1.17730	+	1.61678i	−0.588650	+	0.808388i
$5$	−2.76208	+	2.76208i	−1.23524	+	1.23524i	−0.273315	+	0.961925i	$0.588120\pi$
$5$	−2.76208	+	2.76208i	−1.23524	+	1.23524i	−0.961925	+	0.273315i	$0.911880\pi$
$6$	1.98942	−	1.42906i	0.812178	−	0.583410i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.79289	−	0.446945i	−0.987436	−	0.158019i
$9$	−2.86205	+	0.899256i	−0.954017	+	0.299752i
$10$	−5.25287	−	1.70987i	−1.66110	−	0.540708i
$11$	−3.92989	−	3.92989i	−1.18491	−	1.18491i	−0.978458	−	0.206448i	$-0.933810\pi$
$11$	−3.92989	−	3.92989i	−1.18491	−	1.18491i	−0.206448	−	0.978458i	$-0.566190\pi$
$12$	3.07715	+	1.59095i	0.888297	+	0.459269i
$13$	−1.26876	+	1.26876i	−0.351891	+	0.351891i	−0.860813	−	0.508922i	$-0.830044\pi$
$13$	−1.26876	+	1.26876i	−0.351891	+	0.351891i	0.508922	+	0.860813i	$0.330044\pi$
$14$	0.641365	+	1.26042i	0.171412	+	0.336861i
$15$	5.45415	+	4.00334i	1.40826	+	1.03366i
$16$	−1.22793	−	3.80686i	−0.306982	−	0.951715i
$17$			7.10884i			1.72415i	0.506783	+	0.862074i	$0.330835\pi$
$17$			7.10884i			1.72415i	−0.506783	+	0.862074i	$0.669165\pi$
$18$	−2.96906	−	3.03063i	−0.699814	−	0.714325i
$19$	−0.652997	−	0.652997i	−0.149808	−	0.149808i	0.628224	−	0.778032i	$-0.283782\pi$
$19$	−0.652997	−	0.652997i	−0.149808	−	0.149808i	−0.778032	+	0.628224i	$0.783782\pi$
$20$	−1.21386	−	7.71746i	−0.271428	−	1.72568i
$21$	−0.262630	−	1.71202i	−0.0573105	−	0.373594i
$22$	2.43280	−	7.47379i	0.518675	−	1.59342i
$23$			3.98276i			0.830464i	0.909716	+	0.415232i	$0.136300\pi$
$23$			3.98276i			0.830464i	−0.909716	+	0.415232i	$0.863700\pi$
$24$	−0.0316852	+	4.89888i	−0.00646772	+	0.999979i
$25$		−	10.2582i		−	2.05163i
$26$	−2.41291	−	0.785428i	−0.473210	−	0.154035i
$27$	2.29121	+	4.66373i	0.440943	+	0.897535i
$28$	−1.17730	+	1.61678i	−0.222489	+	0.305542i
$29$	−0.280064	−	0.280064i	−0.0520065	−	0.0520065i	0.680625	−	0.732632i	$-0.261708\pi$
$29$	−0.280064	−	0.280064i	−0.0520065	−	0.0520065i	−0.732632	+	0.680625i	$0.761708\pi$
$30$	−1.54778	+	9.44211i	−0.282584	+	1.72389i
$31$			2.51952i			0.452518i	0.974067	+	0.226259i	$0.0726496\pi$
$31$			2.51952i			0.452518i	−0.974067	+	0.226259i	$0.927350\pi$
$32$	4.01068	−	3.98929i	0.708995	−	0.705213i
$33$	−5.69595	+	7.76016i	−0.991538	+	1.35087i
$34$	−8.96010	+	4.55937i	−1.53665	+	0.781925i
$35$	−2.76208	+	2.76208i	−0.466877	+	0.466877i
$36$	1.91560	−	5.68599i	0.319267	−	0.947665i
$37$	2.94433	+	2.94433i	0.484045	+	0.484045i	0.906421	−	0.422376i	$-0.138804\pi$
$37$	2.94433	+	2.94433i	0.484045	+	0.484045i	−0.422376	+	0.906421i	$0.638804\pi$
$38$	0.404238	−	1.24186i	0.0655761	−	0.201456i
$39$	2.50536	+	1.83893i	0.401179	+	0.294465i
$40$	8.94869	−	6.47969i	1.41491	−	1.02453i
$41$	−5.39610			−0.842729			−0.421365	−	0.906891i	$-0.638449\pi$
$41$	−5.39610			−0.842729			−0.421365	+	0.906891i	$0.638449\pi$
$42$	1.98942	−	1.42906i	0.306974	−	0.220508i
$43$	−1.15575	+	1.15575i	−0.176251	+	0.176251i	−0.789719	−	0.613469i	$-0.789774\pi$
$43$	−1.15575	+	1.15575i	−0.176251	+	0.176251i	0.613469	+	0.789719i	$0.289774\pi$
$44$	10.9804	−	1.72709i	1.65536	−	0.260368i
$45$	5.42140	−	10.3890i	0.808174	−	1.54871i
$46$	−5.01994	+	2.55441i	−0.740150	+	0.376627i
$47$	5.00105			0.729477			0.364739	−	0.931110i	$-0.381158\pi$
$47$	5.00105			0.729477			0.364739	+	0.931110i	$0.381158\pi$
$48$	−6.19495	+	3.10203i	−0.894164	+	0.447740i
$49$	1.00000			0.142857
$50$	12.9296	−	6.57924i	1.82852	−	0.930445i
$51$	12.1705	−	1.86699i	1.70421	−	0.261431i
$52$	−0.557588	−	3.54501i	−0.0773236	−	0.491605i
$53$	6.25168	−	6.25168i	0.858734	−	0.858734i	−0.132455	−	0.991189i	$-0.542286\pi$
$53$	6.25168	−	6.25168i	0.858734	−	0.858734i	0.991189	+	0.132455i	$0.0422861\pi$
$54$	−4.40874	+	5.87903i	−0.599954	+	0.800035i
$55$	21.7093			2.92728
$56$	−2.79289	−	0.446945i	−0.373216	−	0.0597256i
$57$	−0.946449	+	1.28944i	−0.125360	+	0.170791i
$58$	0.173374	−	0.532620i	0.0227651	−	0.0699365i
$59$	1.75981	+	1.75981i	0.229108	+	0.229108i	0.812320	−	0.583212i	$-0.198204\pi$
$59$	1.75981	+	1.75981i	0.229108	+	0.229108i	−0.583212	+	0.812320i	$0.698204\pi$
$60$	−12.8937	+	4.10500i	−1.66457	+	0.529953i
$61$	−2.02736	+	2.02736i	−0.259577	+	0.259577i	−0.824882	−	0.565305i	$-0.808759\pi$
$61$	−2.02736	+	2.02736i	−0.259577	+	0.259577i	0.565305	+	0.824882i	$0.308759\pi$
$62$	−3.17564	+	1.61593i	−0.403307	+	0.205223i
$63$	−2.86205	+	0.899256i	−0.360585	+	0.113296i
$64$	7.60048	+	2.49654i	0.950060	+	0.312067i
$65$		−	7.00883i		−	0.869339i
$66$	−13.4342	−	2.20218i	−1.65364	−	0.271069i
$67$	−0.986955	−	0.986955i	−0.120576	−	0.120576i	0.644244	−	0.764820i	$-0.277172\pi$
$67$	−0.986955	−	0.986955i	−0.120576	−	0.120576i	−0.764820	+	0.644244i	$0.777172\pi$
$68$	−11.4934	−	8.36924i	−1.39378	−	1.01492i
$69$	6.81859	−	1.04599i	0.820861	−	0.125923i
$70$	−5.25287	−	1.70987i	−0.627839	−	0.204368i
$71$			5.74760i			0.682115i	0.940042	+	0.341057i	$0.110785\pi$
$71$			5.74760i			0.682115i	−0.940042	+	0.341057i	$0.889215\pi$
$72$	8.39532	−	1.23234i	0.989397	−	0.145233i
$73$			0.913402i			0.106906i	0.998570	+	0.0534528i	$0.0170227\pi$
$73$			0.913402i			0.106906i	−0.998570	+	0.0534528i	$0.982977\pi$
$74$	−1.82269	+	5.59948i	−0.211884	+	0.650926i
$75$	−17.5622	+	2.69410i	−2.02791	+	0.311088i
$76$	1.82452	−	0.286976i	0.209287	−	0.0329184i
$77$	−3.92989	−	3.92989i	−0.447852	−	0.447852i
$78$	−0.710970	+	4.33723i	−0.0805015	+	0.491094i
$79$		−	3.77043i		−	0.424206i	−0.977247	−	0.212103i	$-0.931969\pi$
$79$		−	3.77043i		−	0.424206i	0.977247	−	0.212103i	$-0.0680313\pi$
$80$	13.9065	+	7.12323i	1.55479	+	0.796401i
$81$	7.38268	−	5.14744i	0.820297	−	0.571937i
$82$	−3.46087	−	6.80133i	−0.382189	−	0.751082i
$83$	−9.11508	+	9.11508i	−1.00051	+	1.00051i	−0.000510506		1.00000i	$0.500162\pi$
$83$	−9.11508	+	9.11508i	−1.00051	+	1.00051i	−1.00000		0.000510506i	$0.999838\pi$
$84$	3.07715	+	1.59095i	0.335745	+	0.173587i
$85$	−19.6352	−	19.6352i	−2.12974	−	2.12974i
$86$	−2.19799	−	0.715470i	−0.237015	−	0.0771511i
$87$	−0.405923	+	0.553029i	−0.0435195	+	0.0592909i
$88$	9.21930	+	12.7322i	0.982781	+	1.35726i
$89$	−2.10538			−0.223170			−0.111585	−	0.993755i	$-0.535593\pi$
$89$	−2.10538			−0.223170			−0.111585	+	0.993755i	$0.535593\pi$
$90$	16.5716	+	0.170053i	1.74680	+	0.0179251i
$91$	−1.26876	+	1.26876i	−0.133002	+	0.133002i
$92$	−6.43923	−	4.68891i	−0.671337	−	0.488853i
$93$	4.31347	−	0.661699i	0.447286	−	0.0686150i
$94$	3.20750	+	6.30340i	0.330828	+	0.650146i
$95$	3.60726			0.370097
$96$	−7.88308	−	5.81868i	−0.804564	−	0.593866i
$97$	11.0425			1.12120			0.560599	−	0.828087i	$-0.310571\pi$
$97$	11.0425			1.12120			0.560599	+	0.828087i	$0.310571\pi$
$98$	0.641365	+	1.26042i	0.0647877	+	0.127321i
$99$	14.7815	+	7.71356i	1.48560	+	0.775242i
$100$	16.5852	+	12.0770i	1.65852	+	1.20770i
$101$	−9.78409	+	9.78409i	−0.973553	+	0.973553i	−0.999659	−	0.0261061i	$-0.991689\pi$
$101$	−9.78409	+	9.78409i	−0.973553	+	0.973553i	0.0261061	+	0.999659i	$0.491689\pi$
$102$	10.1589	+	14.1425i	1.00588	+	1.40031i
$103$	−8.98633			−0.885449			−0.442725	−	0.896658i	$-0.645988\pi$
$103$	−8.98633			−0.885449			−0.442725	+	0.896658i	$0.645988\pi$
$104$	4.11058	−	2.97644i	0.403075	−	0.291864i
$105$	5.45415	+	4.00334i	0.532271	+	0.390686i
$106$	11.8893	+	3.87011i	1.15479	+	0.375898i
$107$	−7.72822	−	7.72822i	−0.747116	−	0.747116i	0.226821	−	0.973936i	$-0.427167\pi$
$107$	−7.72822	−	7.72822i	−0.747116	−	0.747116i	−0.973936	+	0.226821i	$0.927167\pi$
$108$	−10.2376	−	1.78624i	−0.985118	−	0.171881i
$109$	−11.7747	+	11.7747i	−1.12781	+	1.12781i	−0.137276	+	0.990533i	$0.543835\pi$
$109$	−11.7747	+	11.7747i	−1.12781	+	1.12781i	−0.990533	+	0.137276i	$0.956165\pi$
$110$	13.9236	+	27.3628i	1.32756	+	2.60894i
$111$	4.26750	−	5.81404i	0.405053	−	0.551844i
$112$	−1.22793	−	3.80686i	−0.116028	−	0.359715i
$113$		−	5.06042i		−	0.476044i	−0.971260	−	0.238022i	$-0.923501\pi$
$113$		−	5.06042i		−	0.476044i	0.971260	−	0.238022i	$-0.0764990\pi$
$114$	−2.23225	−	0.365917i	−0.209070	−	0.0342713i
$115$	−11.0007	−	11.0007i	−1.02582	−	1.02582i
$116$	0.782519	−	0.123081i	0.0726551	−	0.0114278i
$117$	2.49032	−	4.77220i	0.230230	−	0.441190i
$118$	−1.08941	+	3.34677i	−0.100288	+	0.308095i
$119$			7.10884i			0.651667i
$120$	−13.4436	−	13.6186i	−1.22722	−	1.24320i
$121$			19.8880i			1.80800i
$122$	−3.85561	−	1.25504i	−0.349070	−	0.113626i
$123$	1.41718	+	9.23825i	0.127782	+	0.832985i
$124$	−4.07349	−	2.96623i	−0.365810	−	0.266375i
$125$	14.5235	+	14.5235i	1.29902	+	1.29902i
$126$	−2.96906	−	3.03063i	−0.264505	−	0.269990i
$127$		−	0.811521i		−	0.0720108i	−0.999352	−	0.0360054i	$-0.988537\pi$
$127$		−	0.811521i		−	0.0720108i	0.999352	−	0.0360054i	$-0.0114634\pi$
$128$	1.72801	+	11.1810i	0.152736	+	0.988267i
$129$	2.28221	+	1.67514i	0.200937	+	0.147488i
$130$	8.83405	−	4.49522i	0.774798	−	0.394257i
$131$	14.6635	−	14.6635i	1.28115	−	1.28115i	0.341142	−	0.940012i	$-0.389186\pi$
$131$	14.6635	−	14.6635i	1.28115	−	1.28115i	0.940012	−	0.341142i	$-0.110814\pi$
$132$	−5.84059	−	18.3451i	−0.508358	−	1.59674i
$133$	−0.652997	−	0.652997i	−0.0566220	−	0.0566220i
$134$	0.610975	−	1.87697i	0.0527802	−	0.162146i
$135$	−19.2101	−	6.55309i	−1.65334	−	0.564001i
$136$	3.17726	−	19.8542i	0.272448	−	1.70249i
$137$	−14.1272			−1.20697			−0.603483	−	0.797376i	$-0.706221\pi$
$137$	−14.1272			−1.20697			−0.603483	+	0.797376i	$0.706221\pi$
$138$	5.69159	+	7.92340i	0.484500	+	0.674484i
$139$	−11.6721	+	11.6721i	−0.990011	+	0.990011i	−0.999951	−	0.00993974i	$-0.996836\pi$
$139$	−11.6721	+	11.6721i	−0.990011	+	0.990011i	0.00993974	+	0.999951i	$0.496836\pi$
$140$	−1.21386	−	7.71746i	−0.102590	−	0.652245i
$141$	−1.31342	−	8.56191i	−0.110610	−	0.721043i
$142$	−7.24437	+	3.68631i	−0.607934	+	0.309349i
$143$	9.97217			0.833914
$144$	6.93773	+	9.79121i	0.578144	+	0.815934i
$145$	1.54712			0.128481
$146$	−1.15127	+	0.585825i	−0.0952796	+	0.0484832i
$147$	−0.262630	−	1.71202i	−0.0216613	−	0.141205i
$148$	−8.22669	+	1.29396i	−0.676230	+	0.106363i
$149$	9.48788	−	9.48788i	0.777278	−	0.777278i	−0.202089	−	0.979367i	$-0.564773\pi$
$149$	9.48788	−	9.48788i	0.777278	−	0.777278i	0.979367	+	0.202089i	$0.0647732\pi$
$150$	−14.6595	−	20.4078i	−1.19694	−	1.66629i
$151$	−8.56314			−0.696858			−0.348429	−	0.937335i	$-0.613285\pi$
$151$	−8.56314			−0.696858			−0.348429	+	0.937335i	$0.613285\pi$
$152$	1.53189	+	2.11560i	0.124253	+	0.171598i
$153$	−6.39267	−	20.3459i	−0.516817	−	1.64487i
$154$	2.43280	−	7.47379i	0.196041	−	0.602255i
$155$	−6.95910	−	6.95910i	−0.558969	−	0.558969i
$156$	−5.92271	+	1.88563i	−0.474196	+	0.150971i
$157$	−7.19844	+	7.19844i	−0.574498	+	0.574498i	−0.933382	−	0.358884i	$-0.883157\pi$
$157$	−7.19844	+	7.19844i	−0.574498	+	0.574498i	0.358884	+	0.933382i	$0.383157\pi$
$158$	4.75231	−	2.41822i	0.378074	−	0.192383i
$159$	−12.3449	−	9.06114i	−0.979014	−	0.718595i
$160$	−0.0590908	+	22.0966i	−0.00467153	+	1.74689i
$161$			3.98276i			0.313886i
$162$	11.2229	+	6.00386i	0.881755	+	0.471708i
$163$	−2.47226	−	2.47226i	−0.193643	−	0.193643i	0.603625	−	0.797268i	$-0.293722\pi$
$163$	−2.47226	−	2.47226i	−0.193643	−	0.193643i	−0.797268	+	0.603625i	$0.793722\pi$
$164$	6.35283	−	8.72428i	0.496073	−	0.681252i
$165$	−5.70151	−	37.1669i	−0.443862	−	2.89344i
$166$	−17.3349	−	5.64270i	−1.34545	−	0.437959i
$167$		−	8.81314i		−	0.681981i	−0.940067	−	0.340990i	$-0.889238\pi$
$167$		−	8.81314i		−	0.681981i	0.940067	−	0.340990i	$-0.110762\pi$
$168$	−0.0316852	+	4.89888i	−0.00244457	+	0.377957i
$169$			9.78050i			0.752346i
$170$	12.1552	−	37.3419i	0.932260	−	2.86399i
$171$	2.45612	+	1.28170i	0.187824	+	0.0980139i
$172$	−0.507924	−	3.22926i	−0.0387288	−	0.246229i
$173$	−3.61856	−	3.61856i	−0.275114	−	0.275114i	0.556041	−	0.831155i	$-0.312320\pi$
$173$	−3.61856	−	3.61856i	−0.275114	−	0.275114i	−0.831155	+	0.556041i	$0.812320\pi$
$174$	−0.957392	−	0.156938i	−0.0725797	−	0.0118975i
$175$		−	10.2582i		−	0.775445i
$176$	−10.1349	+	19.7861i	−0.763948	+	1.49144i
$177$	2.55066	−	3.47501i	0.191719	−	0.261198i
$178$	−1.35032	−	2.65366i	−0.101211	−	0.198900i
$179$	−1.44438	+	1.44438i	−0.107958	+	0.107958i	−0.759023	−	0.651064i	$-0.774323\pi$
$179$	−1.44438	+	1.44438i	−0.107958	+	0.107958i	0.651064	+	0.759023i	$0.274323\pi$
$180$	10.4141	+	20.9962i	0.776223	+	1.56496i
$181$	9.19999	+	9.19999i	0.683830	+	0.683830i	0.960861	−	0.277031i	$-0.0893506\pi$
$181$	9.19999	+	9.19999i	0.683830	+	0.683830i	−0.277031	+	0.960861i	$0.589351\pi$
$182$	−2.41291	−	0.785428i	−0.178856	−	0.0582198i
$183$	4.00334	+	2.93845i	0.295936	+	0.217217i
$184$	1.78008	−	11.1234i	0.131229	−	0.820030i
$185$	−16.2650			−1.19582
$186$	3.60053	+	5.01238i	0.264003	+	0.367525i
$187$	27.9369	−	27.9369i	2.04295	−	2.04295i
$188$	−5.88773	+	8.08557i	−0.429407	+	0.589701i
$189$	2.29121	+	4.66373i	0.166661	+	0.339236i
$190$	2.31357	+	4.54665i	0.167844	+	0.329848i
$191$	2.75575			0.199399			0.0996995	−	0.995018i	$-0.468212\pi$
$191$	2.75575			0.199399			0.0996995	+	0.995018i	$0.468212\pi$
$192$	2.27802	−	13.6679i	0.164402	−	0.986393i
$193$	−12.7111			−0.914965			−0.457483	−	0.889219i	$-0.651249\pi$
$193$	−12.7111			−0.914965			−0.457483	+	0.889219i	$0.651249\pi$
$194$	7.08229	+	13.9182i	0.508479	+	0.999267i
$195$	−11.9993	+	1.84073i	−0.859287	+	0.131817i
$196$	−1.17730	+	1.61678i	−0.0840929	+	0.115484i
$197$	−12.4779	+	12.4779i	−0.889010	+	0.889010i	−0.994428	−	0.105418i	$-0.966382\pi$
$197$	−12.4779	+	12.4779i	−0.889010	+	0.889010i	0.105418	+	0.994428i	$0.466382\pi$
$198$	−0.241951	+	23.5781i	−0.0171947	+	1.67562i
$199$	16.2474			1.15175			0.575876	−	0.817537i	$-0.304661\pi$
$199$	16.2474			1.15175			0.575876	+	0.817537i	$0.304661\pi$
$200$	−4.58484	+	28.6500i	−0.324197	+	2.02586i
$201$	−1.43049	+	1.94889i	−0.100899	+	0.137464i
$202$	−18.6072	−	6.05685i	−1.30920	−	0.426159i
$203$	−0.280064	−	0.280064i	−0.0196566	−	0.0196566i
$204$	−11.3098	+	21.8750i	−0.791847	+	1.53156i
$205$	14.9045	−	14.9045i	1.04097	−	1.04097i
$206$	−5.76352	−	11.3265i	−0.401564	−	0.789156i
$207$	−3.58152	−	11.3989i	−0.248933	−	0.792276i
$208$	6.38794	+	3.27205i	0.442924	+	0.226876i
$209$			5.13240i			0.355016i
$210$	−1.54778	+	9.44211i	−0.106807	+	0.651567i
$211$	18.8613	+	18.8613i	1.29846	+	1.29846i	0.929408	+	0.369055i	$0.120319\pi$
$211$	18.8613	+	18.8613i	1.29846	+	1.29846i	0.369055	+	0.929408i	$0.379681\pi$
$212$	2.74745	+	17.4677i	0.188696	+	1.19968i
$213$	9.84003	−	1.50949i	0.674228	−	0.103429i
$214$	4.78417	−	14.6974i	0.327039	−	1.00469i
$215$		−	6.38456i		−	0.435423i
$216$	−4.31466	−	14.0493i	−0.293575	−	0.955936i
$217$			2.51952i			0.171036i
$218$	−22.3929	−	7.28912i	−1.51664	−	0.493682i
$219$	1.56377	−	0.239886i	0.105670	−	0.0162100i
$220$	−25.5584	+	35.0991i	−1.72315	+	2.36638i
$221$	−9.01942	−	9.01942i	−0.606712	−	0.606712i
$222$	10.0651	+	1.64990i	0.675528	+	0.110734i
$223$		−	14.1500i		−	0.947552i	−0.880645	−	0.473776i	$-0.842891\pi$
$223$		−	14.1500i		−	0.947552i	0.880645	−	0.473776i	$-0.157109\pi$
$224$	4.01068	−	3.98929i	0.267975	−	0.266546i
$225$	9.22472	+	29.3594i	0.614982	+	1.95729i
$226$	6.37823	−	3.24558i	0.424274	−	0.215893i
$227$	6.21650	−	6.21650i	0.412603	−	0.412603i	−0.470041	−	0.882645i	$-0.655761\pi$
$227$	6.21650	−	6.21650i	0.412603	−	0.412603i	0.882645	+	0.470041i	$0.155761\pi$
$228$	−0.970483	−	3.04826i	−0.0642718	−	0.201876i
$229$	−2.04458	−	2.04458i	−0.135110	−	0.135110i	0.636318	−	0.771427i	$-0.280457\pi$
$229$	−2.04458	−	2.04458i	−0.135110	−	0.135110i	−0.771427	+	0.636318i	$0.780457\pi$
$230$	6.81000	−	20.9210i	0.449038	−	1.37949i
$231$	−5.69595	+	7.76016i	−0.374766	+	0.510581i
$232$	0.657014	+	0.907361i	0.0431351	+	0.0595711i
$233$	25.5534			1.67406			0.837030	−	0.547157i	$-0.184290\pi$
$233$	25.5534			1.67406			0.837030	+	0.547157i	$0.184290\pi$
$234$	7.61216	+	0.0781136i	0.497622	+	0.00510645i
$235$	−13.8133	+	13.8133i	−0.901079	+	0.901079i
$236$	−4.91704	+	0.773392i	−0.320072	+	0.0503435i
$237$	−6.45506	+	0.990226i	−0.419301	+	0.0643221i
$238$	−8.96010	+	4.55937i	−0.580797	+	0.295540i
$239$	20.4220			1.32099			0.660493	−	0.750832i	$-0.270347\pi$
$239$	20.4220			1.32099			0.660493	+	0.750832i	$0.270347\pi$
$240$	8.54288	−	25.6790i	0.551440	−	1.65757i
$241$	−9.12556			−0.587829			−0.293914	−	0.955832i	$-0.594958\pi$
$241$	−9.12556			−0.587829			−0.293914	+	0.955832i	$0.594958\pi$
$242$	−25.0672	+	12.7555i	−1.61138	+	0.819954i
$243$	−10.7514	−	11.2874i	−0.689705	−	0.724090i
$244$	−0.890976	−	5.66461i	−0.0570389	−	0.362640i
$245$	−2.76208	+	2.76208i	−0.176463	+	0.176463i
$246$	−10.7351	+	7.71133i	−0.684446	+	0.491656i
$247$	1.65699			0.105432
$248$	1.12609	−	7.03673i	0.0715065	−	0.446833i
$249$	17.9991	+	13.2113i	1.14065	+	0.837235i
$250$	−8.99078	+	27.6205i	−0.568627	+	1.74687i
$251$	−13.0159	−	13.0159i	−0.821554	−	0.821554i	0.164777	−	0.986331i	$-0.447309\pi$
$251$	−13.0159	−	13.0159i	−0.821554	−	0.821554i	−0.986331	+	0.164777i	$0.947309\pi$
$252$	1.91560	−	5.68599i	0.120671	−	0.358184i
$253$	15.6518	−	15.6518i	0.984021	−	0.984021i
$254$	1.02285	−	0.520481i	0.0641796	−	0.0326579i
$255$	−28.4591	+	38.7727i	−1.78218	+	2.42804i
$256$	−12.9844	+	9.34909i	−0.811525	+	0.584318i
$257$		−	4.90026i		−	0.305670i	−0.988252	−	0.152835i	$-0.951160\pi$
$257$		−	4.90026i		−	0.305670i	0.988252	−	0.152835i	$-0.0488402\pi$
$258$	−0.647644	+	3.95091i	−0.0403206	+	0.245973i
$259$	2.94433	+	2.94433i	0.182952	+	0.182952i
$260$	11.3317	+	8.25150i	0.702763	+	0.511737i
$261$	1.05341	+	0.549708i	0.0652042	+	0.0340261i
$262$	27.8867	+	9.07744i	1.72285	+	0.560806i
$263$			3.50904i			0.216377i	0.994130	+	0.108188i	$0.0345050\pi$
$263$			3.50904i			0.216377i	−0.994130	+	0.108188i	$0.965495\pi$
$264$	19.3765	−	19.1275i	1.19254	−	1.17722i
$265$			34.5353i			2.12148i
$266$	0.404238	−	1.24186i	0.0247854	−	0.0761432i
$267$	0.552935	+	3.60446i	0.0338391	+	0.220590i
$268$	2.75763	−	0.433742i	0.168449	−	0.0264950i
$269$	9.49745	+	9.49745i	0.579070	+	0.579070i	0.934647	−	0.355577i	$-0.115716\pi$
$269$	9.49745	+	9.49745i	0.579070	+	0.579070i	−0.355577	+	0.934647i	$0.615716\pi$
$270$	−4.06106	−	28.4156i	−0.247148	−	1.72932i
$271$		−	0.198651i		−	0.0120672i	−0.999982	−	0.00603358i	$-0.998079\pi$
$271$		−	0.198651i		−	0.0120672i	0.999982	−	0.00603358i	$-0.00192056\pi$
$272$	27.0624	−	8.72914i	1.64090	−	0.529282i
$273$	2.50536	+	1.83893i	0.151631	+	0.111297i
$274$	−9.06068	−	17.8061i	−0.547375	−	1.07571i
$275$	−40.3134	+	40.3134i	−2.43099	+	2.43099i
$276$	−6.33639	+	12.2556i	−0.381406	+	0.737699i
$277$	15.9895	+	15.9895i	0.960714	+	0.960714i	0.999257	−	0.0385425i	$-0.0122715\pi$
$277$	15.9895	+	15.9895i	0.960714	+	0.960714i	−0.0385425	+	0.999257i	$0.512271\pi$
$278$	−22.1977	−	7.22560i	−1.33133	−	0.433363i
$279$	−2.26569	−	7.21098i	−0.135643	−	0.431710i
$280$	8.94869	−	6.47969i	0.534786	−	0.387236i
$281$	−9.46558			−0.564669			−0.282335	−	0.959316i	$-0.591109\pi$
$281$	−9.46558			−0.564669			−0.282335	+	0.959316i	$0.591109\pi$
$282$	9.94919	−	7.14677i	0.592466	−	0.425584i
$283$	8.84357	−	8.84357i	0.525696	−	0.525696i	−0.393590	−	0.919286i	$-0.628767\pi$
$283$	8.84357	−	8.84357i	0.525696	−	0.525696i	0.919286	+	0.393590i	$0.128767\pi$
$284$	−9.29258	−	6.76666i	−0.551413	−	0.401527i
$285$	−0.947372	−	6.17571i	−0.0561175	−	0.365818i
$286$	6.39580	+	12.5691i	0.378192	+	0.743226i
$287$	−5.39610			−0.318522
$288$	−7.89139	+	15.0242i	−0.465004	+	0.885308i
$289$	−33.5356			−1.97268
$290$	0.992267	+	1.95001i	0.0582679	+	0.114509i
$291$	−2.90009	−	18.9051i	−0.170006	−	1.10823i
$292$	−1.47677	−	1.07535i	−0.0864212	−	0.0629300i
$293$	18.8459	−	18.8459i	1.10099	−	1.10099i	0.106696	−	0.994292i	$-0.465973\pi$
$293$	18.8459	−	18.8459i	1.10099	−	1.10099i	0.994292	−	0.106696i	$-0.0340271\pi$
$294$	1.98942	−	1.42906i	0.116025	−	0.0833442i
$295$	−9.72146			−0.566005
$296$	−6.90725	−	9.53916i	−0.401476	−	0.554452i
$297$	9.32374	−	27.3321i	0.541018	−	1.58597i
$298$	18.0439	+	5.87348i	1.04525	+	0.340242i
$299$	−5.05317	−	5.05317i	−0.292232	−	0.292232i
$300$	16.3203	−	31.5660i	0.942251	−	1.82246i
$301$	−1.15575	+	1.15575i	−0.0666164	+	0.0666164i
$302$	−5.49210	−	10.7931i	−0.316035	−	0.621074i
$303$	19.3202	+	14.1810i	1.10992	+	0.814677i
$304$	−1.68404	+	3.28770i	−0.0965861	+	0.188562i
$305$		−	11.1995i		−	0.641281i
$306$	21.5442	−	21.1066i	1.23160	−	1.20658i
$307$	2.17003	+	2.17003i	0.123850	+	0.123850i	0.766315	−	0.642465i	$-0.222088\pi$
$307$	2.17003	+	2.17003i	0.123850	+	0.123850i	−0.642465	+	0.766315i	$0.722088\pi$
$308$	10.9804	−	1.72709i	0.625666	−	0.0984099i
$309$	2.36008	+	15.3848i	0.134260	+	0.875211i
$310$	4.30804	−	13.2347i	0.244680	−	0.751680i
$311$			30.2350i			1.71447i	0.514926	+	0.857235i	$0.327819\pi$
$311$			30.2350i			1.71447i	−0.514926	+	0.857235i	$0.672181\pi$
$312$	−6.17530	−	6.25570i	−0.349607	−	0.354159i
$313$			18.5885i			1.05069i	0.850891	+	0.525343i	$0.176063\pi$
$313$			18.5885i			1.05069i	−0.850891	+	0.525343i	$0.823937\pi$
$314$	−13.6899	−	4.45620i	−0.772564	−	0.251478i
$315$	5.42140	−	10.3890i	0.305461	−	0.585356i
$316$	6.09594	+	4.43893i	0.342923	+	0.249709i
$317$	19.3130	+	19.3130i	1.08473	+	1.08473i	0.996061	+	0.0886652i	$0.0282601\pi$
$317$	19.3130	+	19.3130i	1.08473	+	1.08473i	0.0886652	+	0.996061i	$0.471740\pi$
$318$	3.50323	−	21.3712i	0.196451	−	1.19844i
$319$			2.20124i			0.123246i
$320$	−27.8888	+	14.0975i	−1.55903	+	0.788074i
$321$	−11.2012	+	15.2606i	−0.625192	+	0.851762i
$322$	−5.01994	+	2.55441i	−0.279750	+	0.142352i
$323$	4.64205	−	4.64205i	0.258291	−	0.258291i
$324$	−0.369382	+	17.9962i	−0.0205212	+	0.999789i
$325$	13.0152	+	13.0152i	0.721951	+	0.721951i
$326$	1.53046	−	4.70171i	0.0847642	−	0.260403i
$327$	23.2509	+	17.0661i	1.28578	+	0.943760i
$328$	15.0707	+	2.41176i	0.832141	+	0.133167i
$329$	5.00105			0.275717
$330$	43.1890	−	31.0238i	2.37748	−	1.70781i
$331$	21.6694	−	21.6694i	1.19106	−	1.19106i	0.214284	−	0.976771i	$-0.431258\pi$
$331$	21.6694	−	21.6694i	1.19106	−	1.19106i	0.976771	−	0.214284i	$-0.0687419\pi$
$332$	−4.00585	−	25.4682i	−0.219850	−	1.39775i
$333$	−11.0745	−	5.77912i	−0.606881	−	0.316694i
$334$	11.1082	−	5.65244i	0.607815	−	0.309288i
$335$	5.45209			0.297880
$336$	−6.19495	+	3.10203i	−0.337962	+	0.169230i
$337$	13.1246			0.714944			0.357472	−	0.933924i	$-0.383639\pi$
$337$	13.1246			0.714944			0.357472	+	0.933924i	$0.383639\pi$
$338$	−12.3275	+	6.27287i	−0.670528	+	0.341199i
$339$	−8.66355	+	1.32902i	−0.470540	+	0.0721822i
$340$	54.8622	−	8.62917i	2.97532	−	0.467983i
$341$	9.90141	−	9.90141i	0.536191	−	0.536191i
$342$	−0.0402030	+	3.91777i	−0.00217393	+	0.211849i
$343$	1.00000			0.0539949
$344$	3.74445	−	2.71133i	0.201887	−	0.146185i
$345$	−15.9444	+	21.7226i	−0.858416	+	1.16950i
$346$	2.24007	−	6.88171i	0.120427	−	0.369963i
$347$	−5.82438	−	5.82438i	−0.312669	−	0.312669i	0.533274	−	0.845943i	$-0.320962\pi$
$347$	−5.82438	−	5.82438i	−0.312669	−	0.312669i	−0.845943	+	0.533274i	$0.820962\pi$
$348$	−0.416230	−	1.30737i	−0.0223123	−	0.0700822i
$349$	−16.4941	+	16.4941i	−0.882909	+	0.882909i	−0.993829	−	0.110920i	$-0.964620\pi$
$349$	−16.4941	+	16.4941i	−0.882909	+	0.882909i	0.110920	+	0.993829i	$0.464620\pi$
$350$	12.9296	−	6.57924i	0.691115	−	0.351675i
$351$	−8.82415	−	3.01016i	−0.470998	−	0.160670i
$352$	−31.4390	−	0.0840743i	−1.67570	−	0.00448118i
$353$		−	15.6060i		−	0.830625i	−0.909679	−	0.415313i	$-0.863672\pi$
$353$		−	15.6060i		−	0.830625i	0.909679	−	0.415313i	$-0.136328\pi$
$354$	6.01587	+	0.986137i	0.319740	+	0.0524126i
$355$	−15.8753	−	15.8753i	−0.842575	−	0.842575i
$356$	2.47867	−	3.40393i	0.131369	−	0.180408i
$357$	12.1705	−	1.86699i	0.644132	−	0.0988117i
$358$	−2.74690	−	0.894147i	−0.145178	−	0.0472571i
$359$		−	9.53840i		−	0.503417i	−0.967803	−	0.251709i	$-0.919008\pi$
$359$		−	9.53840i		−	0.503417i	0.967803	−	0.251709i	$-0.0809925\pi$
$360$	−19.7847	+	26.5924i	−1.04275	+	1.40154i
$361$		−	18.1472i		−	0.955115i
$362$	−5.69526	+	17.4964i	−0.299336	+	0.919589i
$363$	34.0487	−	5.22318i	1.78710	−	0.274146i
$364$	−0.557588	−	3.54501i	−0.0292256	−	0.185809i
$365$	−2.52289	−	2.52289i	−0.132054	−	0.132054i
$366$	−1.13607	+	6.93050i	−0.0593832	+	0.362263i
$367$			12.3806i			0.646260i	0.946355	+	0.323130i	$0.104735\pi$
$367$			12.3806i			0.646260i	−0.946355	+	0.323130i	$0.895265\pi$
$368$	15.1618	−	4.89054i	0.790365	−	0.254937i
$369$	15.4439	−	4.85248i	0.803978	−	0.252610i
$370$	−10.4318	−	20.5006i	−0.542323	−	1.06578i
$371$	6.25168	−	6.25168i	0.324571	−	0.324571i
$372$	−4.00843	+	7.75293i	−0.207827	+	0.401971i
$373$	3.59111	+	3.59111i	0.185941	+	0.185941i	0.793939	−	0.607998i	$-0.208027\pi$
$373$	3.59111	+	3.59111i	0.185941	+	0.185941i	−0.607998	+	0.793939i	$0.708027\pi$
$374$	53.1300	+	17.2944i	2.74729	+	0.894272i
$375$	21.0503	−	28.6789i	1.08703	−	1.48097i
$376$	−13.9674	−	2.23519i	−0.720312	−	0.115271i
$377$	0.710667			0.0366012
$378$	−4.40874	+	5.87903i	−0.226761	+	0.302385i
$379$	−15.3273	+	15.3273i	−0.787313	+	0.787313i	−0.981053	−	0.193740i	$-0.937938\pi$
$379$	−15.3273	+	15.3273i	−0.787313	+	0.787313i	0.193740	+	0.981053i	$0.437938\pi$
$380$	−4.24683	+	5.83213i	−0.217858	+	0.299182i
$381$	−1.38934	+	0.213129i	−0.0711782	+	0.0109189i
$382$	1.76744	+	3.47339i	0.0904302	+	0.177714i
$383$	4.41723			0.225710			0.112855	−	0.993611i	$-0.464000\pi$
$383$	4.41723			0.225710			0.112855	+	0.993611i	$0.464000\pi$
$384$	18.6883	−	5.89484i	0.953681	−	0.300820i
$385$	21.7093			1.10641
$386$	−8.15246	−	16.0213i	−0.414949	−	0.815462i
$387$	2.26850	−	4.34714i	0.115315	−	0.220977i
$388$	−13.0004	+	17.8533i	−0.659994	+	0.906363i
$389$	−23.4765	+	23.4765i	−1.19031	+	1.19031i	−0.213325	+	0.976981i	$0.568429\pi$
$389$	−23.4765	+	23.4765i	−1.19031	+	1.19031i	−0.976981	+	0.213325i	$0.931571\pi$
$390$	−10.0160	−	13.9435i	−0.507181	−	0.706058i
$391$	−28.3128			−1.43184
$392$	−2.79289	−	0.446945i	−0.141062	−	0.0225741i
$393$	−28.9553	−	21.2532i	−1.46060	−	1.07208i
$394$	−23.7302	−	7.72443i	−1.19551	−	0.389151i
$395$	10.4142	+	10.4142i	0.523997	+	0.523997i
$396$	−29.8734	+	14.8172i	−1.50119	+	0.744593i
$397$	−14.2331	+	14.2331i	−0.714340	+	0.714340i	−0.967440	−	0.253100i	$-0.918550\pi$
$397$	−14.2331	+	14.2331i	−0.714340	+	0.714340i	0.253100	+	0.967440i	$0.418550\pi$
$398$	10.4206	+	20.4786i	0.522335	+	1.02650i
$399$	−0.946449	+	1.28944i	−0.0473817	+	0.0645528i
$400$	−39.0514	+	12.5963i	−1.95257	+	0.629814i
$401$		−	35.8009i		−	1.78781i	−0.448257	−	0.893905i	$-0.647955\pi$
$401$		−	35.8009i		−	1.78781i	0.448257	−	0.893905i	$-0.352045\pi$
$402$	−3.37388	−	0.553056i	−0.168274	−	0.0275839i
$403$	−3.19666	−	3.19666i	−0.159237	−	0.159237i
$404$	−4.29986	−	27.3375i	−0.213926	−	1.36009i
$405$	−6.17391	+	34.6092i	−0.306784	+	1.71974i
$406$	0.173374	−	0.532620i	0.00860440	−	0.0264335i
$407$		−	23.1418i		−	1.14710i
$408$	−34.8253	−	0.225245i	−1.72411	−	0.0111513i
$409$		−	11.6596i		−	0.576532i	−0.957550	−	0.288266i	$-0.906921\pi$
$409$		−	11.6596i		−	0.576532i	0.957550	−	0.288266i	$-0.0930787\pi$
$410$	28.3450	+	9.22662i	1.39986	+	0.455670i
$411$	3.71021	+	24.1860i	0.183011	+	1.19301i
$412$	10.5796	−	14.5289i	0.521220	−	0.715787i
$413$	1.75981	+	1.75981i	0.0865945	+	0.0865945i
$414$	12.0703	−	11.8251i	0.593221	−	0.581170i
$415$		−	50.3532i		−	2.47174i
$416$	−0.0271433	+	10.1500i	−0.00133081	+	0.497647i
$417$	23.0483	+	16.9174i	1.12868	+	0.828449i
$418$	−6.46897	+	3.29175i	−0.316408	+	0.161005i
$419$	−14.9672	+	14.9672i	−0.731196	+	0.731196i	−0.970857	−	0.239661i	$-0.922964\pi$
$419$	−14.9672	+	14.9672i	−0.731196	+	0.731196i	0.239661	+	0.970857i	$0.422964\pi$
$420$	−12.8937	+	4.10500i	−0.629147	+	0.200303i
$421$	−3.24667	−	3.24667i	−0.158233	−	0.158233i	0.623550	−	0.781783i	$-0.285690\pi$
$421$	−3.24667	−	3.24667i	−0.158233	−	0.158233i	−0.781783	+	0.623550i	$0.785690\pi$
$422$	−11.6761	+	35.8700i	−0.568383	+	1.74612i
$423$	−14.3132	+	4.49722i	−0.695934	+	0.218662i
$424$	−20.2544	+	14.6661i	−0.983641	+	0.712248i
$425$	72.9237			3.53732
$426$	8.21364	+	11.4344i	0.397952	+	0.553999i
$427$	−2.02736	+	2.02736i	−0.0981111	+	0.0981111i
$428$	21.5932	−	3.39636i	1.04375	−	0.164169i
$429$	−2.61899	−	17.0726i	−0.126446	−	0.824272i
$430$	8.04720	−	4.09484i	0.388071	−	0.197470i
$431$	0.423649			0.0204065			0.0102032	−	0.999948i	$-0.496752\pi$
$431$	0.423649			0.0204065			0.0102032	+	0.999948i	$0.496752\pi$
$432$	14.9407	−	14.4490i	0.718837	−	0.695179i
$433$	16.1430			0.775783			0.387891	−	0.921705i	$-0.373204\pi$
$433$	16.1430			0.775783			0.387891	+	0.921705i	$0.373204\pi$
$434$	−3.17564	+	1.61593i	−0.152436	+	0.0775671i
$435$	−0.406319	−	2.64870i	−0.0194815	−	0.126995i
$436$	−5.17467	−	32.8993i	−0.247822	−	1.57559i
$437$	2.60073	−	2.60073i	0.124410	−	0.124410i
$438$	1.30530	+	1.81714i	0.0623698	+	0.0868264i
$439$	−16.3312			−0.779444			−0.389722	−	0.920933i	$-0.627429\pi$
$439$	−16.3312			−0.779444			−0.389722	+	0.920933i	$0.627429\pi$
$440$	−60.6318	−	9.70288i	−2.89051	−	0.462567i
$441$	−2.86205	+	0.899256i	−0.136288	+	0.0428217i
$442$	5.58348	−	17.1530i	0.265579	−	0.815883i
$443$	−1.31668	−	1.31668i	−0.0625575	−	0.0625575i	0.675136	−	0.737693i	$-0.264085\pi$
$443$	−1.31668	−	1.31668i	−0.0625575	−	0.0625575i	−0.737693	+	0.675136i	$0.764085\pi$
$444$	4.37586	+	13.7445i	0.207669	+	0.652283i
$445$	5.81523	−	5.81523i	0.275668	−	0.275668i
$446$	17.8349	−	9.07530i	0.844505	−	0.429728i
$447$	−18.7353	−	13.7517i	−0.886148	−	0.650432i
$448$	7.60048	+	2.49654i	0.359089	+	0.117950i
$449$			10.5577i			0.498249i	0.968471	+	0.249124i	$0.0801428\pi$
$449$			10.5577i			0.498249i	−0.968471	+	0.249124i	$0.919857\pi$
$450$	−31.0887	+	30.4571i	−1.46553	+	1.43576i
$451$	21.2061	+	21.2061i	0.998554	+	0.998554i
$452$	8.18156	+	5.95763i	0.384828	+	0.280223i
$453$	2.24893	+	14.6603i	0.105664	+	0.688801i
$454$	11.8224	+	3.84833i	0.554854	+	0.180611i
$455$		−	7.00883i		−	0.328579i
$456$	3.21964	−	3.17826i	0.150773	−	0.148836i
$457$		−	16.5719i		−	0.775201i	−0.921827	−	0.387600i	$-0.873304\pi$
$457$		−	16.5719i		−	0.775201i	0.921827	−	0.387600i	$-0.126696\pi$
$458$	1.26570	−	3.88835i	0.0591423	−	0.181691i
$459$	−33.1537	+	16.2878i	−1.54748	+	0.760251i
$460$	30.7368	−	4.83454i	1.43311	−	0.225411i
$461$	19.2689	+	19.2689i	0.897444	+	0.897444i	0.995209	−	0.0977653i	$-0.0311695\pi$
$461$	19.2689	+	19.2689i	0.897444	+	0.897444i	−0.0977653	+	0.995209i	$0.531169\pi$
$462$	−13.4342	−	2.20218i	−0.625017	−	0.102454i
$463$			0.0613759i			0.00285238i	0.999999	+	0.00142619i	$0.000453971\pi$
$463$			0.0613759i			0.00285238i	−0.999999	+	0.00142619i	$0.999546\pi$
$464$	−0.722266	+	1.41006i	−0.0335304	+	0.0654605i
$465$	−10.0865	+	13.7418i	−0.467749	+	0.637261i
$466$	16.3891	+	32.2080i	0.759209	+	1.49200i
$467$	−6.97512	+	6.97512i	−0.322770	+	0.322770i	−0.849829	−	0.527059i	$-0.823295\pi$
$467$	−6.97512	+	6.97512i	−0.322770	+	0.322770i	0.527059	+	0.849829i	$0.323295\pi$
$468$	4.78372	+	9.64459i	0.221128	+	0.445821i
$469$	−0.986955	−	0.986955i	−0.0455733	−	0.0455733i
$470$	−26.2699	−	8.55113i	−1.21174	−	0.394434i
$471$	14.2144	+	10.4334i	0.654966	+	0.480745i
$472$	−4.12841	−	5.70149i	−0.190026	−	0.262432i
$473$	9.08395			0.417680
$474$	−5.38815	−	7.50097i	−0.247486	−	0.344531i
$475$	−6.69855	+	6.69855i	−0.307351	+	0.307351i
$476$	−11.4934	−	8.36924i	−0.526799	−	0.383604i
$477$	−12.2708	+	23.5145i	−0.561839	+	1.07665i
$478$	13.0979	+	25.7402i	0.599086	+	1.17733i
$479$	−28.9163			−1.32122			−0.660610	−	0.750729i	$-0.729702\pi$
$479$	−28.9163			−1.32122			−0.660610	+	0.750729i	$0.729702\pi$
$480$	37.8454	−	5.70205i	1.72740	−	0.260262i
$481$	−7.47131			−0.340662
$482$	−5.85282	−	11.5020i	−0.266589	−	0.523902i
$483$	6.81859	−	1.04599i	0.310256	−	0.0475943i
$484$	−32.1544	−	23.4142i	−1.46157	−	1.06428i
$485$	−30.5003	+	30.5003i	−1.38495	+	1.38495i
$486$	7.33129	−	20.7907i	0.332554	−	0.943084i
$487$	5.49646			0.249068			0.124534	−	0.992215i	$-0.460256\pi$
$487$	5.49646			0.249068			0.124534	+	0.992215i	$0.460256\pi$
$488$	6.56833	−	4.75609i	0.297334	−	0.215298i
$489$	−3.58328	+	4.88186i	−0.162042	+	0.220766i
$490$	−5.25287	−	1.70987i	−0.237301	−	0.0772440i
$491$	25.5668	+	25.5668i	1.15381	+	1.15381i	0.985782	+	0.168032i	$0.0537411\pi$
$491$	25.5668	+	25.5668i	1.15381	+	1.15381i	0.168032	+	0.985782i	$0.446259\pi$
$492$	−16.6046	−	8.58494i	−0.748594	−	0.387039i
$493$	1.99093	−	1.99093i	0.0896669	−	0.0896669i
$494$	1.06274	+	2.08850i	0.0478148	+	0.0939661i
$495$	−62.1332	+	19.5222i	−2.79268	+	0.877459i
$496$	9.59145	−	3.09378i	0.430669	−	0.138915i
$497$			5.74760i			0.257815i
$498$	−5.10778	+	31.1597i	−0.228885	+	1.39630i
$499$	2.47543	+	2.47543i	0.110815	+	0.110815i	0.760340	−	0.649525i	$-0.225032\pi$
$499$	2.47543	+	2.47543i	0.110815	+	0.110815i	−0.649525	+	0.760340i	$0.725032\pi$
$500$	−40.5797	+	6.38271i	−1.81478	+	0.285443i
$501$	−15.0883	+	2.31459i	−0.674095	+	0.103408i
$502$	8.05748	−	24.7533i	0.359623	−	1.10479i
$503$			28.0431i			1.25038i	0.780472	+	0.625191i	$0.214979\pi$
$503$			28.0431i			1.25038i	−0.780472	+	0.625191i	$0.785021\pi$
$504$	8.39532	−	1.23234i	0.373957	−	0.0548930i
$505$		−	54.0489i		−	2.40514i
$506$	29.7663	+	9.68927i	1.32327	+	0.430741i
$507$	16.7444	−	2.56865i	0.743647	−	0.114078i
$508$	1.31205	+	0.955404i	0.0582127	+	0.0423892i
$509$	−2.29808	−	2.29808i	−0.101861	−	0.101861i	0.654340	−	0.756201i	$-0.272947\pi$
$509$	−2.29808	−	2.29808i	−0.101861	−	0.101861i	−0.756201	+	0.654340i	$0.772947\pi$
$510$	−67.1225	−	11.0029i	−2.97223	−	0.487216i
$511$			0.913402i			0.0404065i
$512$	−20.1115	−	10.3696i	−0.888811	−	0.458274i
$513$	1.54925	−	4.54155i	0.0684010	−	0.200514i
$514$	6.17636	−	3.14285i	0.272428	−	0.138625i
$515$	24.8210	−	24.8210i	1.09374	−	1.09374i
$516$	−5.39517	+	1.71768i	−0.237509	+	0.0756165i
$517$	−19.6535	−	19.6535i	−0.864362	−	0.864362i
$518$	−1.82269	+	5.59948i	−0.0800845	+	0.246027i
$519$	−5.24471	+	7.14539i	−0.230217	+	0.313648i
$520$	−3.13257	+	19.5749i	−0.137372	+	0.858417i
$521$	19.1601			0.839420			0.419710	−	0.907658i	$-0.362132\pi$
$521$	19.1601			0.839420			0.419710	+	0.907658i	$0.362132\pi$
$522$	−0.0172427	+	1.68029i	−0.000754690	+	0.0735445i
$523$	−6.72307	+	6.72307i	−0.293979	+	0.293979i	−0.838650	−	0.544671i	$-0.816655\pi$
$523$	−6.72307	+	6.72307i	−0.293979	+	0.293979i	0.544671	+	0.838650i	$0.316655\pi$
$524$	6.44423	+	40.9709i	0.281517	+	1.78982i
$525$	−17.5622	+	2.69410i	−0.766479	+	0.117580i
$526$	−4.42286	+	2.25058i	−0.192846	+	0.0981299i
$527$	−17.9108			−0.780208
$528$	36.5361	+	12.1548i	1.59003	+	0.528970i
$529$	7.13760			0.310330
$530$	−43.5288	+	22.1497i	−1.89077	+	0.962122i
$531$	−6.61918	−	3.45414i	−0.287248	−	0.149897i
$532$	1.82452	−	0.286976i	0.0791031	−	0.0124420i
$533$	6.84636	−	6.84636i	0.296549	−	0.296549i
$534$	−4.18849	+	3.00871i	−0.181254	+	0.130200i
$535$	42.6919			1.84573
$536$	2.31534	+	3.19757i	0.100008	+	0.138114i
$537$	2.85215	+	2.09348i	0.123080	+	0.0903403i
$538$	−5.87941	+	18.0621i	−0.253479	+	0.778712i
$539$	−3.92989	−	3.92989i	−0.169272	−	0.169272i
$540$	33.2109	−	23.3434i	1.42917	−	1.00454i
$541$	0.396767	−	0.396767i	0.0170584	−	0.0170584i	−0.698526	−	0.715585i	$-0.746160\pi$
$541$	0.396767	−	0.396767i	0.0170584	−	0.0170584i	0.715585	+	0.698526i	$0.246160\pi$
$542$	0.250382	−	0.127408i	0.0107548	−	0.00547262i
$543$	13.3344	−	18.1668i	0.572234	−	0.779611i
$544$	28.3592	+	28.5113i	1.21589	+	1.22241i
$545$		−	65.0452i		−	2.78623i
$546$	−0.710970	+	4.33723i	−0.0304267	+	0.185616i
$547$	1.62002	+	1.62002i	0.0692672	+	0.0692672i	0.740892	−	0.671624i	$-0.234403\pi$
$547$	1.62002	+	1.62002i	0.0692672	+	0.0692672i	−0.671624	+	0.740892i	$0.734403\pi$
$548$	16.6319	−	22.8405i	0.710480	−	0.975696i
$549$	3.97930	−	7.62554i	0.169832	−	0.325450i
$550$	−76.6674	−	24.9561i	−3.26911	−	1.06413i
$551$			0.365761i			0.0155820i
$552$	−19.5111	−	0.126195i	−0.830446	−	0.00537121i
$553$		−	3.77043i		−	0.160335i
$554$	−9.89830	+	30.4085i	−0.420539	+	1.29193i
$555$	4.27166	+	27.8460i	0.181322	+	1.18200i
$556$	−5.12958	−	32.6126i	−0.217542	−	1.38308i
$557$	3.91321	+	3.91321i	0.165808	+	0.165808i	0.785134	−	0.619326i	$-0.212594\pi$
$557$	3.91321	+	3.91321i	0.165808	+	0.165808i	−0.619326	+	0.785134i	$0.712594\pi$
$558$	7.63571	−	7.48059i	0.323245	−	0.316679i
$559$		−	2.93274i		−	0.124042i
$560$	13.9065	+	7.12323i	0.587656	+	0.301011i
$561$	−55.1658	−	40.4916i	−2.32910	−	1.70956i
$562$	−6.07090	−	11.9306i	−0.256085	−	0.503261i
$563$	21.9917	−	21.9917i	0.926839	−	0.926839i	−0.0706616	−	0.997500i	$-0.522511\pi$
$563$	21.9917	−	21.9917i	0.926839	−	0.926839i	0.997500	+	0.0706616i	$0.0225111\pi$
$564$	15.3890	+	7.95643i	0.647993	+	0.335026i
$565$	13.9773	+	13.9773i	0.588028	+	0.588028i
$566$	16.8185	+	5.47462i	0.706936	+	0.230116i
$567$	7.38268	−	5.14744i	0.310043	−	0.216172i
$568$	2.56886	−	16.0524i	0.107787	−	0.673545i
$569$	−38.8292			−1.62781			−0.813903	−	0.581001i	$-0.802661\pi$
$569$	−38.8292			−1.62781			−0.813903	+	0.581001i	$0.802661\pi$
$570$	7.17636	−	5.15497i	0.300585	−	0.215918i
$571$	28.6026	−	28.6026i	1.19698	−	1.19698i	0.221918	−	0.975065i	$-0.428768\pi$
$571$	28.6026	−	28.6026i	1.19698	−	1.19698i	0.975065	−	0.221918i	$-0.0712318\pi$
$572$	−11.7402	+	16.1228i	−0.490884	+	0.674126i
$573$	−0.723741	−	4.71791i	−0.0302347	−	0.197094i
$574$	−3.46087	−	6.80133i	−0.144454	−	0.283882i
$575$	40.8559			1.70381
$576$	−23.9980	−	0.310444i	−0.999916	−	0.0129352i
$577$	−23.0517			−0.959655			−0.479828	−	0.877363i	$-0.659301\pi$
$577$	−23.0517			−0.959655			−0.479828	+	0.877363i	$0.659301\pi$
$578$	−21.5086	−	42.2689i	−0.894640	−	1.75815i
$579$	3.33831	+	21.7617i	0.138735	+	0.904386i
$580$	−1.82142	+	2.50134i	−0.0756304	+	0.103863i
$581$	−9.11508	+	9.11508i	−0.378157	+	0.378157i
$582$	21.9682	−	15.7804i	0.910613	−	0.654118i
$583$	−49.1367			−2.03504
$584$	0.408241	−	2.55103i	0.0168931	−	0.105562i
$585$	6.30274	+	20.0596i	0.260586	+	0.829364i
$586$	35.8407	+	11.6666i	1.48057	+	0.481941i
$587$	0.0987095	+	0.0987095i	0.00407418	+	0.00407418i	0.709141	−	0.705067i	$-0.249083\pi$
$587$	0.0987095	+	0.0987095i	0.00407418	+	0.00407418i	−0.705067	+	0.709141i	$0.749083\pi$
$588$	3.07715	+	1.59095i	0.126900	+	0.0656098i
$589$	1.64523	−	1.64523i	0.0677907	−	0.0677907i
$590$	−6.23501	−	12.2531i	−0.256691	−	0.504452i
$591$	24.6394	+	18.0853i	1.01353	+	0.743931i
$592$	7.59324	−	14.8241i	0.312080	−	0.609267i
$593$		−	1.95818i		−	0.0804128i	−0.999191	−	0.0402064i	$-0.987198\pi$
$593$		−	1.95818i		−	0.0804128i	0.999191	−	0.0402064i	$-0.0128015\pi$
$594$	40.4298	−	5.77807i	1.65885	−	0.237077i
$595$	−19.6352	−	19.6352i	−0.804964	−	0.804964i
$596$	4.16969	+	26.5099i	0.170797	+	1.08589i
$597$	−4.26706	−	27.8160i	−0.174639	−	1.13843i
$598$	3.12817	−	9.61003i	0.127920	−	0.392983i
$599$		−	28.3381i		−	1.15786i	−0.815377	−	0.578931i	$-0.803470\pi$
$599$		−	28.3381i		−	1.15786i	0.815377	−	0.578931i	$-0.196530\pi$
$600$	50.2535	+	0.325032i	2.05159	+	0.0132694i
$601$		−	1.19282i		−	0.0486562i	−0.999704	−	0.0243281i	$-0.992255\pi$
$601$		−	1.19282i		−	0.0486562i	0.999704	−	0.0243281i	$-0.00774464\pi$
$602$	−2.19799	−	0.715470i	−0.0895833	−	0.0291604i
$603$	3.71224	+	1.93719i	0.151174	+	0.0788885i
$604$	10.0814	−	13.8447i	0.410206	−	0.563332i
$605$	−54.9323	−	54.9323i	−2.23331	−	2.23331i
$606$	−5.48267	+	33.4467i	−0.222718	+	1.35868i
$607$			22.0892i			0.896571i	0.893890	+	0.448285i	$0.147965\pi$
$607$			22.0892i			0.896571i	−0.893890	+	0.448285i	$0.852035\pi$
$608$	−5.22395	−	0.0139699i	−0.211859	−	0.000566555i
$609$	−0.405923	+	0.553029i	−0.0164488	+	0.0224099i
$610$	14.1160	−	7.18296i	0.571541	−	0.290830i
$611$	−6.34513	+	6.34513i	−0.256696	+	0.256696i
$612$	40.4208	+	13.6177i	1.63391	+	0.550463i
$613$	−1.62425	−	1.62425i	−0.0656027	−	0.0656027i	0.673544	−	0.739147i	$-0.264771\pi$
$613$	−1.62425	−	1.62425i	−0.0656027	−	0.0656027i	−0.739147	+	0.673544i	$0.764771\pi$
$614$	−1.34336	+	4.12693i	−0.0542137	+	0.166549i
$615$	−29.4311	−	21.6024i	−1.18678	−	0.871094i
$616$	9.21930	+	12.7322i	0.371456	+	0.512994i
$617$	7.82504			0.315024			0.157512	−	0.987517i	$-0.449653\pi$
$617$	7.82504			0.315024			0.157512	+	0.987517i	$0.449653\pi$
$618$	−17.8776	+	12.8420i	−0.719143	+	0.516580i
$619$	−5.36556	+	5.36556i	−0.215660	+	0.215660i	−0.806667	−	0.591007i	$-0.798731\pi$
$619$	−5.36556	+	5.36556i	−0.215660	+	0.215660i	0.591007	+	0.806667i	$0.298731\pi$
$620$	19.4443	−	3.05835i	0.780900	−	0.122826i
$621$	−18.5745	+	9.12534i	−0.745370	+	0.366187i
$622$	−38.1087	+	19.3917i	−1.52802	+	0.777536i
$623$	−2.10538			−0.0843503
$624$	3.92417	−	11.7956i	0.157092	−	0.472204i
$625$	−28.9392			−1.15757
$626$	−23.4293	+	11.9220i	−0.936423	+	0.476501i
$627$	8.78680	−	1.34792i	0.350911	−	0.0538308i
$628$	−3.16353	−	20.1130i	−0.126239	−	0.802595i
$629$	−20.9308	+	20.9308i	−0.834566	+	0.834566i
$630$	16.5716	+	0.170053i	0.660229	+	0.00677506i
$631$	38.0571			1.51503			0.757514	−	0.652819i	$-0.226414\pi$
$631$	38.0571			1.51503			0.757514	+	0.652819i	$0.226414\pi$
$632$	−1.68518	+	10.5304i	−0.0670327	+	0.418877i
$633$	27.3374	−	37.2444i	1.08656	−	1.48033i
$634$	−11.9557	+	36.7291i	−0.474823	+	1.45870i
$635$	2.24148	+	2.24148i	0.0889506	+	0.0889506i
$636$	29.1835	−	9.29123i	1.15720	−	0.368421i
$637$	−1.26876	+	1.26876i	−0.0502701	+	0.0502701i
$638$	−2.77448	+	1.41180i	−0.109843	+	0.0558936i
$639$	−5.16857	−	16.4499i	−0.204465	−	0.650749i
$640$	−35.6556	−	26.1098i	−1.40941	−	1.03208i
$641$			19.4732i			0.769144i	0.923095	+	0.384572i	$0.125651\pi$
$641$			19.4732i			0.769144i	−0.923095	+	0.384572i	$0.874349\pi$
$642$	−26.4188	−	4.33064i	−1.04267	−	0.170917i
$643$	13.0510	+	13.0510i	0.514680	+	0.514680i	0.915957	−	0.401277i	$-0.131433\pi$
$643$	13.0510	+	13.0510i	0.514680	+	0.514680i	−0.401277	+	0.915957i	$0.631433\pi$
$644$	−6.43923	−	4.68891i	−0.253741	−	0.184769i
$645$	−10.9305	+	1.67677i	−0.430389	+	0.0660229i
$646$	8.82817	+	2.87367i	0.347340	+	0.113063i
$647$		−	24.7212i		−	0.971891i	−0.873989	−	0.485945i	$-0.838475\pi$
$647$		−	24.7212i		−	0.971891i	0.873989	−	0.485945i	$-0.161525\pi$
$648$	−22.9196	+	11.0766i	−0.900368	+	0.435129i
$649$		−	13.8317i		−	0.542941i
$650$	−8.05705	+	24.7520i	−0.316023	+	0.970853i
$651$	4.31347	−	0.661699i	0.169058	−	0.0259340i
$652$	6.90769	−	1.08650i	0.270526	−	0.0425505i
$653$	29.4389	+	29.4389i	1.15203	+	1.15203i	0.986145	+	0.165888i	$0.0530489\pi$
$653$	29.4389	+	29.4389i	1.15203	+	1.15203i	0.165888	+	0.986145i	$0.446951\pi$
$654$	−6.59813	+	40.2514i	−0.258007	+	1.57396i
$655$			81.0034i			3.16506i
$656$	6.62601	+	20.5422i	0.258702	+	0.802038i
$657$	−0.821383	−	2.61420i	−0.0320452	−	0.101990i
$658$	3.20750	+	6.30340i	0.125041	+	0.245732i
$659$	−2.12621	+	2.12621i	−0.0828252	+	0.0828252i	−0.747306	−	0.664480i	$-0.768653\pi$
$659$	−2.12621	+	2.12621i	−0.0828252	+	0.0828252i	0.664480	+	0.747306i	$0.268653\pi$
$660$	66.8029	+	34.5385i	2.60030	+	1.34441i
$661$	−19.0840	−	19.0840i	−0.742282	−	0.742282i	0.230735	−	0.973017i	$-0.425887\pi$
$661$	−19.0840	−	19.0840i	−0.742282	−	0.742282i	−0.973017	+	0.230735i	$0.925887\pi$
$662$	41.2104	+	13.4144i	1.60169	+	0.521367i
$663$	−13.0727	+	17.8102i	−0.507701	+	0.691692i
$664$	29.5314	−	21.3835i	1.14604	−	0.829840i
$665$	3.60726			0.139883
$666$	0.181273	−	17.6651i	0.00702420	−	0.684508i
$667$	1.11543	−	1.11543i	0.0431895	−	0.0431895i
$668$	14.2489	+	10.3757i	0.551305	+	0.401448i
$669$	−24.2251	+	3.71620i	−0.936596	+	0.143677i
$670$	3.49679	+	6.87191i	0.135093	+	0.265485i
$671$	15.9346			0.615149
$672$	−7.88308	−	5.81868i	−0.304096	−	0.224460i
$673$	18.1038			0.697851			0.348925	−	0.937150i	$-0.386547\pi$
$673$	18.1038			0.697851			0.348925	+	0.937150i	$0.386547\pi$
$674$	8.41768	+	16.5425i	0.324237	+	0.637193i
$675$	47.8413	−	23.5036i	1.84141	−	0.904654i
$676$	−15.8129	−	11.5146i	−0.608187	−	0.442869i
$677$	21.8857	−	21.8857i	0.841136	−	0.841136i	−0.147871	−	0.989007i	$-0.547242\pi$
$677$	21.8857	−	21.8857i	0.841136	−	0.841136i	0.989007	+	0.147871i	$0.0472421\pi$
$678$	−7.23162	−	10.0673i	−0.277729	−	0.386632i
$679$	11.0425			0.423773
$680$	46.0631	+	63.6148i	1.76644	+	2.43952i
$681$	−12.2754	−	9.01016i	−0.470395	−	0.345270i
$682$	18.8303	+	6.12948i	0.721050	+	0.234710i
$683$	21.1021	+	21.1021i	0.807449	+	0.807449i	0.984247	−	0.176798i	$-0.0565739\pi$
$683$	21.1021	+	21.1021i	0.807449	+	0.807449i	−0.176798	+	0.984247i	$0.556574\pi$
$684$	−4.96381	+	2.46205i	−0.189796	+	0.0941389i
$685$	39.0204	−	39.0204i	1.49089	−	1.49089i
$686$	0.641365	+	1.26042i	0.0244874	+	0.0481229i
$687$	−2.96341	+	4.03734i	−0.113061	+	0.154034i
$688$	5.81897	+	2.98061i	0.221846	+	0.113635i
$689$			15.8638i			0.604361i
$690$	−37.6057	−	6.16443i	−1.43162	−	0.234676i
$691$	−22.6731	−	22.6731i	−0.862526	−	0.862526i	0.129105	−	0.991631i	$-0.458790\pi$
$691$	−22.6731	−	22.6731i	−0.862526	−	0.862526i	−0.991631	+	0.129105i	$0.958790\pi$
$692$	10.1105	−	1.59026i	0.384344	−	0.0604528i
$693$	14.7815	+	7.71356i	0.561503	+	0.293014i
$694$	3.60559	−	11.0767i	0.136866	−	0.420466i
$695$		−	64.4783i		−	2.44580i
$696$	1.38087	−	1.36312i	0.0523418	−	0.0516691i
$697$		−	38.3600i		−	1.45299i
$698$	−31.3682	−	10.2107i	−1.18730	−	0.386480i
$699$	−6.71108	−	43.7481i	−0.253836	−	1.65470i
$700$	16.5852	+	12.0770i	0.626860	+	0.456466i
$701$	13.6997	+	13.6997i	0.517431	+	0.517431i	0.916793	−	0.399362i	$-0.130768\pi$
$701$	13.6997	+	13.6997i	0.517431	+	0.517431i	−0.399362	+	0.916793i	$0.630768\pi$
$702$	−1.86545	−	13.0527i	−0.0704067	−	0.492643i
$703$		−	3.84528i		−	0.145027i
$704$	−20.0579	−	39.6801i	−0.755961	−	1.49550i
$705$	27.2765	+	20.0209i	1.02729	+	0.754031i
$706$	19.6701	−	10.0092i	0.740294	−	0.376700i
$707$	−9.78409	+	9.78409i	−0.367968	+	0.367968i
$708$	2.61542	+	8.21497i	0.0982937	+	0.308738i
$709$	24.7783	+	24.7783i	0.930567	+	0.930567i	0.997741	−	0.0671741i	$-0.0213983\pi$
$709$	24.7783	+	24.7783i	0.930567	+	0.930567i	−0.0671741	+	0.997741i	$0.521398\pi$
$710$	9.82765	−	30.1914i	0.368825	−	1.13306i
$711$	3.39058	+	10.7912i	0.127157	+	0.404700i
$712$	5.88010	+	0.940990i	0.220366	+	0.0352651i
$713$	−10.0346			−0.375800
$714$	10.1589	+	14.1425i	0.380188	+	0.529269i
$715$	−27.5439	+	27.5439i	−1.03008	+	1.03008i
$716$	−0.634770	−	4.03571i	−0.0237225	−	0.150822i
$717$	−5.36341	−	34.9629i	−0.200300	−	1.30571i
$718$	12.0224	−	6.11760i	0.448670	−	0.228307i
$719$	20.2382			0.754759			0.377379	−	0.926059i	$-0.376825\pi$
$719$	20.2382			0.754759			0.377379	+	0.926059i	$0.376825\pi$
$720$	−46.2067	−	7.88154i	−1.72202	−	0.293728i
$721$	−8.98633			−0.334668
$722$	22.8730	−	11.6390i	0.851246	−	0.433158i
$723$	2.39664	+	15.6232i	0.0891321	+	0.581032i
$724$	−25.7055	+	4.04316i	−0.955336	+	0.150263i
$725$	−2.87294	+	2.87294i	−0.106698	+	0.106698i
$726$	28.4211	+	39.5656i	1.05481	+	1.46842i
$727$	−31.6117			−1.17241			−0.586206	−	0.810162i	$-0.699379\pi$
$727$	−31.6117			−1.17241			−0.586206	+	0.810162i	$0.699379\pi$
$728$	4.11058	−	2.97644i	0.152348	−	0.110314i
$729$	−16.5007	+	21.3711i	−0.611138	+	0.791524i
$730$	1.56180	−	4.79799i	0.0578047	−	0.177581i
$731$	−8.21606	−	8.21606i	−0.303882	−	0.303882i
$732$	−9.46395	+	3.01307i	−0.349798	+	0.111366i
$733$	4.40384	−	4.40384i	0.162660	−	0.162660i	−0.621084	−	0.783744i	$-0.713308\pi$
$733$	4.40384	−	4.40384i	0.162660	−	0.162660i	0.783744	+	0.621084i	$0.213308\pi$
$734$	−15.6047	+	7.94047i	−0.575979	+	0.293088i
$735$	5.45415	+	4.00334i	0.201179	+	0.147666i
$736$	15.8884	+	15.9736i	0.585654	+	0.588795i
$737$			7.75724i			0.285742i
$738$	16.0213	+	16.3536i	0.589754	+	0.601983i
$739$	25.7232	+	25.7232i	0.946243	+	0.946243i	0.998627	−	0.0523842i	$-0.0166820\pi$
$739$	25.7232	+	25.7232i	0.946243	+	0.946243i	−0.0523842	+	0.998627i	$0.516682\pi$
$740$	19.1488	−	26.2968i	0.703922	−	0.966690i
$741$	−0.435175	−	2.83681i	−0.0159866	−	0.104213i
$742$	11.8893	+	3.87011i	0.436471	+	0.142076i
$743$		−	34.9069i		−	1.28061i	−0.768121	−	0.640305i	$-0.778808\pi$
$743$		−	34.9069i		−	1.28061i	0.768121	−	0.640305i	$-0.221192\pi$
$744$	−12.3428	−	0.0798314i	−0.452509	−	0.00292676i
$745$			52.4126i			1.92025i
$746$	−2.22308	+	6.82951i	−0.0813928	+	0.250046i
$747$	17.8910	−	34.2846i	0.654599	−	1.25441i
$748$	12.2776	+	78.0579i	0.448913	+	2.85408i
$749$	−7.72822	−	7.72822i	−0.282383	−	0.282383i
$750$	49.6482	+	8.13847i	1.81290	+	0.297175i
$751$			47.1826i			1.72172i	0.508845	+	0.860858i	$0.330072\pi$
$751$			47.1826i			1.72172i	−0.508845	+	0.860858i	$0.669928\pi$
$752$	−6.14092	−	19.0383i	−0.223936	−	0.694255i
$753$	−18.8651	+	25.7018i	−0.687483	+	0.936626i
$754$	0.455798	+	0.895737i	0.0165992	+	0.0326208i
$755$	23.6521	−	23.6521i	0.860787	−	0.860787i
$756$	−10.2376	−	1.78624i	−0.372339	−	0.0649650i
$757$	−7.03526	−	7.03526i	−0.255701	−	0.255701i	0.567602	−	0.823303i	$-0.307871\pi$
$757$	−7.03526	−	7.03526i	−0.255701	−	0.255701i	−0.823303	+	0.567602i	$0.807871\pi$
$758$	−29.1493	−	9.48841i	−1.05875	−	0.344635i
$759$	−30.9069	−	22.6856i	−1.12185	−	0.823437i
$760$	−10.0747	−	1.61225i	−0.365447	−	0.0584823i
$761$	−35.0753			−1.27148			−0.635739	−	0.771904i	$-0.719305\pi$
$761$	−35.0753			−1.27148			−0.635739	+	0.771904i	$0.719305\pi$
$762$	−1.15971	−	1.61446i	−0.0420118	−	0.0584856i
$763$	−11.7747	+	11.7747i	−0.426272	+	0.426272i
$764$	−3.24435	+	4.45543i	−0.117376	+	0.161192i
$765$	73.8540	+	38.5399i	2.67020	+	1.39341i
$766$	2.83306	+	5.56756i	0.102363	+	0.201164i
$767$	−4.46555			−0.161242
$768$	19.4160	+	19.7742i	0.700613	+	0.713541i
$769$	−38.8510			−1.40100			−0.700502	−	0.713650i	$-0.747041\pi$
$769$	−38.8510			−1.40100			−0.700502	+	0.713650i	$0.747041\pi$
$770$	13.9236	+	27.3628i	0.501772	+	0.986086i
$771$	−8.38935	+	1.28695i	−0.302135	+	0.0463484i
$772$	14.9648	−	20.5510i	0.538595	−	0.739647i
$773$	−34.2875	+	34.2875i	−1.23324	+	1.23324i	−0.270523	+	0.962713i	$0.587197\pi$
$773$	−34.2875	+	34.2875i	−1.23324	+	1.23324i	−0.962713	+	0.270523i	$0.912803\pi$
$774$	6.93415	+	0.0711561i	0.249243	+	0.00255765i
$775$	25.8456			0.928402
$776$	−30.8406	−	4.93540i	−1.10711	−	0.177171i
$777$	4.26750	−	5.81404i	0.153096	−	0.208577i
$778$	−44.6472	−	14.5332i	−1.60068	−	0.521039i
$779$	3.52363	+	3.52363i	0.126247	+	0.126247i
$780$	11.1507	−	21.5672i	0.399260	−	0.772231i
$781$	22.5874	−	22.5874i	0.808241	−	0.808241i
$782$	−18.1589	−	35.6860i	−0.649360	−	1.27613i
$783$	0.664457	−	1.94783i	0.0237458	−	0.0696096i
$784$	−1.22793	−	3.80686i	−0.0438545	−	0.135959i
$785$		−	39.7653i		−	1.41929i
$786$	8.21692	−	50.1268i	0.293088	−	1.78796i
$787$	−36.3051	−	36.3051i	−1.29414	−	1.29414i	−0.932205	−	0.361931i	$-0.882118\pi$
$787$	−36.3051	−	36.3051i	−1.29414	−	1.29414i	−0.361931	−	0.932205i	$-0.617882\pi$
$788$	−5.48370	−	34.8641i	−0.195349	−	1.24198i
$789$	6.00756	−	0.921578i	0.213875	−	0.0328091i
$790$	−6.44694	+	19.8056i	−0.229372	+	0.704651i
$791$		−	5.06042i		−	0.179928i
$792$	−37.8356	−	28.1497i	−1.34443	−	1.00025i
$793$		−	5.14448i		−	0.182686i
$794$	−27.0683	−	8.81103i	−0.960618	−	0.312692i
$795$	59.1252	−	9.06998i	2.09695	−	0.321679i
$796$	−19.1281	+	26.2685i	−0.677979	+	0.931062i
$797$	−17.0156	−	17.0156i	−0.602723	−	0.602723i	0.338312	−	0.941034i	$-0.390144\pi$
$797$	−17.0156	−	17.0156i	−0.602723	−	0.602723i	−0.941034	+	0.338312i	$0.890144\pi$
$798$	−2.23225	−	0.365917i	−0.0790209	−	0.0129533i
$799$			35.5516i			1.25773i
$800$	−40.9228	−	41.1423i	−1.44684	−	1.45460i
$801$	6.02571	−	1.89328i	0.212908	−	0.0668957i
$802$	45.1240	−	22.9614i	1.59338	−	0.810796i
$803$	3.58957	−	3.58957i	0.126673	−	0.126673i
$804$	−1.46681	−	4.60721i	−0.0517304	−	0.162484i
$805$	−11.0007	−	11.0007i	−0.387724	−	0.387724i
$806$	1.97890	−	6.07935i	0.0697037	−	0.214136i
$807$	13.7656	−	18.7542i	0.484570	−	0.660178i
$808$	31.6988	−	22.9529i	1.11516	−	0.807481i
$809$	−19.0095			−0.668337			−0.334168	−	0.942513i	$-0.608455\pi$
$809$	−19.0095			−0.668337			−0.334168	+	0.942513i	$0.608455\pi$
$810$	−47.5817	+	14.4154i	−1.67185	+	0.506506i
$811$	7.33718	−	7.33718i	0.257643	−	0.257643i	−0.566452	−	0.824095i	$-0.691684\pi$
$811$	7.33718	−	7.33718i	0.257643	−	0.257643i	0.824095	+	0.566452i	$0.191684\pi$
$812$	0.782519	−	0.123081i	0.0274610	−	0.00431930i
$813$	−0.340094	+	0.0521715i	−0.0119276	+	0.00182973i
$814$	29.1683	−	14.8423i	1.02235	−	0.520224i
$815$	13.6572			0.478390
$816$	−22.0519	−	44.0389i	−0.771970	−	1.54167i
$817$	1.50940			0.0528074
$818$	14.6960	−	7.47809i	0.513834	−	0.261465i
$819$	2.49032	−	4.77220i	0.0870187	−	0.166754i
$820$	6.55014	+	41.6442i	0.228741	+	1.45428i
$821$	−19.4973	+	19.4973i	−0.680460	+	0.680460i	−0.960104	−	0.279644i	$-0.909784\pi$
$821$	−19.4973	+	19.4973i	−0.680460	+	0.680460i	0.279644	+	0.960104i	$0.409784\pi$
$822$	−28.1049	+	20.1885i	−0.980271	+	0.704155i
$823$	−48.4184			−1.68776			−0.843879	−	0.536534i	$-0.819733\pi$
$823$	−48.4184			−1.68776			−0.843879	+	0.536534i	$0.819733\pi$
$824$	25.0978	+	4.01640i	0.874325	+	0.139918i
$825$	79.6051	+	58.4301i	2.77149	+	2.03427i
$826$	−1.08941	+	3.34677i	−0.0379055	+	0.116449i
$827$	−10.0314	−	10.0314i	−0.348826	−	0.348826i	0.510846	−	0.859672i	$-0.329332\pi$
$827$	−10.0314	−	10.0314i	−0.348826	−	0.348826i	−0.859672	+	0.510846i	$0.829332\pi$
$828$	22.6460	+	7.62938i	0.787001	+	0.265139i
$829$	−9.00803	+	9.00803i	−0.312862	+	0.312862i	−0.846017	−	0.533156i	$-0.821006\pi$
$829$	−9.00803	+	9.00803i	−0.312862	+	0.312862i	0.533156	+	0.846017i	$0.321006\pi$
$830$	63.4660	−	32.2948i	2.20294	−	1.12097i
$831$	23.1751	−	31.5737i	0.803934	−	1.09528i
$832$	−12.8107	+	6.47568i	−0.444131	+	0.224504i
$833$			7.10884i			0.246307i
$834$	−6.54063	+	39.9007i	−0.226483	+	1.38165i
$835$	24.3426	+	24.3426i	0.842410	+	0.842410i
$836$	−8.29795	−	6.04238i	−0.286990	−	0.208980i
$837$	−11.7503	+	5.77273i	−0.406151	+	0.199535i
$838$	−28.4644	−	9.26546i	−0.983285	−	0.320070i
$839$			45.7743i			1.58030i	0.612911	+	0.790152i	$0.289998\pi$
$839$			45.7743i			1.58030i	−0.612911	+	0.790152i	$0.710002\pi$
$840$	−13.4436	−	13.6186i	−0.463847	−	0.469887i
$841$		−	28.8431i		−	0.994591i
$842$	2.00985	−	6.17446i	0.0692642	−	0.212786i
$843$	2.48594	+	16.2053i	0.0856204	+	0.558140i
$844$	−52.6998	+	8.28905i	−1.81400	+	0.285321i
$845$	−27.0145	−	27.0145i	−0.929327	−	0.929327i
$846$	−14.8484	−	15.1563i	−0.510498	−	0.521084i
$847$			19.8880i			0.683360i
$848$	−31.4759	−	16.1227i	−1.08089	−	0.553655i
$849$	−17.4630	−	12.8178i	−0.599328	−	0.439907i
$850$	46.7708	+	91.9143i	1.60422	+	3.15263i
$851$	−11.7266	+	11.7266i	−0.401982	+	0.401982i
$852$	−9.14417	+	17.6862i	−0.313274	+	0.605921i
$853$	−13.8350	−	13.8350i	−0.473700	−	0.473700i	0.429410	−	0.903110i	$-0.358722\pi$
$853$	−13.8350	−	13.8350i	−0.473700	−	0.473700i	−0.903110	+	0.429410i	$0.858722\pi$
$854$	−3.85561	−	1.25504i	−0.131936	−	0.0429467i
$855$	−10.3242	+	3.24385i	−0.353079	+	0.110937i
$856$	18.1300	+	25.0382i	0.619670	+	0.855787i
$857$	−0.198042			−0.00676499			−0.00338250	−	0.999994i	$-0.501077\pi$
$857$	−0.198042			−0.00676499			−0.00338250	+	0.999994i	$0.501077\pi$
$858$	19.8388	−	14.2508i	0.677287	−	0.486514i
$859$	9.93654	−	9.93654i	0.339030	−	0.339030i	−0.516972	−	0.856002i	$-0.672941\pi$
$859$	9.93654	−	9.93654i	0.339030	−	0.339030i	0.856002	+	0.516972i	$0.172941\pi$
$860$	10.3224	+	7.51654i	0.351991	+	0.256312i
$861$	1.41718	+	9.23825i	0.0482972	+	0.314839i
$862$	0.271714	+	0.533975i	0.00925462	+	0.0181873i
$863$	41.3690			1.40822			0.704108	−	0.710093i	$-0.251347\pi$
$863$	41.3690			1.40822			0.704108	+	0.710093i	$0.251347\pi$
$864$	27.7943	+	9.56445i	0.945580	+	0.325389i
$865$	19.9895			0.679663
$866$	10.3536	+	20.3469i	0.351828	+	0.691416i
$867$	8.80745	+	57.4138i	0.299117	+	1.94988i
$868$	−4.07349	−	2.96623i	−0.138263	−	0.100680i
$869$	−14.8174	+	14.8174i	−0.502644	+	0.502644i
$870$	3.07787	−	2.21092i	0.104350	−	0.0749571i
$871$	2.50442			0.0848589
$872$	38.1480	−	27.6227i	1.29185	−	0.935424i
$873$	−31.6043	+	9.93006i	−1.06964	+	0.336082i
$874$	4.94602	+	1.60999i	0.167302	+	0.0544586i
$875$	14.5235	+	14.5235i	0.490984	+	0.490984i
$876$	−1.45318	+	2.81068i	−0.0490984	+	0.0949640i
$877$	−35.0042	+	35.0042i	−1.18201	+	1.18201i	−0.202784	+	0.979223i	$0.564999\pi$
$877$	−35.0042	+	35.0042i	−1.18201	+	1.18201i	−0.979223	+	0.202784i	$0.935001\pi$
$878$	−10.4742	−	20.5841i	−0.353489	−	0.694679i
$879$	−37.2141	−	27.3151i	−1.25520	−	0.921315i
$880$	−26.6574	−	82.6444i	−0.898622	−	2.78594i
$881$			36.6416i			1.23449i	0.786772	+	0.617244i	$0.211751\pi$
$881$			36.6416i			1.23449i	−0.786772	+	0.617244i	$0.788249\pi$
$882$	−2.96906	−	3.03063i	−0.0999734	−	0.102046i
$883$	−0.637898	−	0.637898i	−0.0214670	−	0.0214670i	0.696292	−	0.717759i	$-0.254832\pi$
$883$	−0.637898	−	0.637898i	−0.0214670	−	0.0214670i	−0.717759	+	0.696292i	$0.754832\pi$
$884$	25.2009	−	3.96381i	0.847599	−	0.133317i
$885$	2.55314	+	16.6434i	0.0858230	+	0.559461i
$886$	0.815094	−	2.50404i	0.0273836	−	0.0841250i
$887$		−	8.74783i		−	0.293723i	−0.989157	−	0.146862i	$-0.953083\pi$
$887$		−	8.74783i		−	0.293723i	0.989157	−	0.146862i	$-0.0469172\pi$
$888$	−14.5172	+	14.3306i	−0.487166	+	0.480905i
$889$		−	0.811521i		−	0.0272175i
$890$	11.0593	+	3.59993i	0.370709	+	0.120670i
$891$	−49.2419	−	8.78424i	−1.64967	−	0.294283i
$892$	22.8773	+	16.6588i	0.765990	+	0.557777i
$893$	−3.26567	−	3.26567i	−0.109281	−	0.109281i
$894$	5.31669	−	32.4341i	0.177817	−	1.08476i
$895$		−	7.97900i		−	0.266709i
$896$	1.72801	+	11.1810i	0.0577286	+	0.373530i
$897$	−7.32404	+	9.97826i	−0.244542	+	0.333164i
$898$	−13.3071	+	6.77135i	−0.444064	+	0.225963i
$899$	0.705625	−	0.705625i	0.0235339	−	0.0235339i
$900$	−58.3279	−	19.6505i	−1.94426	−	0.655018i
$901$	44.4422	+	44.4422i	1.48058	+	1.48058i
$902$	−13.1276	+	40.3293i	−0.437102	+	1.34282i
$903$	2.28221	+	1.67514i	0.0759472	+	0.0557452i
$904$	−2.26173	+	14.1332i	−0.0752240	+	0.470063i
$905$	−50.8222			−1.68939
$906$	−17.0357	+	12.2372i	−0.565973	+	0.406554i
$907$	19.7335	−	19.7335i	0.655241	−	0.655241i	−0.299009	−	0.954250i	$-0.596656\pi$
$907$	19.7335	−	19.7335i	0.655241	−	0.655241i	0.954250	+	0.299009i	$0.0966562\pi$
$908$	2.73200	+	17.3694i	0.0906644	+	0.576423i
$909$	19.2042	−	36.8010i	0.636962	−	1.22061i
$910$	8.83405	−	4.49522i	0.292846	−	0.149015i
$911$	−21.9542			−0.727374			−0.363687	−	0.931521i	$-0.618482\pi$
$911$	−21.9542			−0.727374			−0.363687	+	0.931521i	$0.618482\pi$
$912$	6.07090	+	2.01966i	0.201027	+	0.0668777i
$913$	71.6425			2.37102
$914$	20.8875	−	10.6286i	0.690897	−	0.351564i
$915$	−19.1738	+	2.94132i	−0.633866	+	0.0972369i
$916$	5.71272	−	0.898542i	0.188753	−	0.0296887i
$917$	14.6635	−	14.6635i	0.484231	−	0.484231i
$918$	−41.7931	−	31.3410i	−1.37938	−	1.03441i
$919$	−8.20968			−0.270812			−0.135406	−	0.990790i	$-0.543234\pi$
$919$	−8.20968			−0.270812			−0.135406	+	0.990790i	$0.543234\pi$
$920$	25.8071	+	35.6405i	0.850834	+	1.17503i
$921$	3.14523	−	4.28506i	0.103639	−	0.141198i
$922$	−11.9285	+	36.6453i	−0.392843	+	1.20685i
$923$	−7.29233	−	7.29233i	−0.240030	−	0.240030i
$924$	−5.84059	−	18.3451i	−0.192141	−	0.603510i
$925$	30.2035	−	30.2035i	0.993084	−	0.993084i
$926$	−0.0773592	+	0.0393644i	−0.00254218	+	0.00129359i
$927$	25.7193	−	8.08101i	0.844734	−	0.265415i
$928$	−2.24050	−	0.00599156i	−0.0735481	−	0.000196683i
$929$		−	38.0207i		−	1.24742i	−0.781657	−	0.623709i	$-0.785625\pi$
$929$		−	38.0207i		−	1.24742i	0.781657	−	0.623709i	$-0.214375\pi$
$930$	−23.7895	−	3.89965i	−0.780090	−	0.127874i
$931$	−0.652997	−	0.652997i	−0.0214011	−	0.0214011i
$932$	−30.0841	+	41.3141i	−0.985436	+	1.35329i
$933$	51.7630	−	7.94060i	1.69465	−	0.259964i
$934$	−13.2652	−	4.31796i	−0.434049	−	0.141288i
$935$			154.328i			5.04707i
$936$	−9.08809	+	12.2152i	−0.297054	+	0.399266i
$937$			11.5227i			0.376430i	0.982128	+	0.188215i	$0.0602701\pi$
$937$			11.5227i			0.376430i	−0.982128	+	0.188215i	$0.939730\pi$
$938$	0.610975	−	1.87697i	0.0199491	−	0.0612853i
$939$	31.8240	−	4.88190i	1.03854	−	0.159315i
$940$	−6.07059	−	38.5954i	−0.198001	−	1.25884i
$941$	32.1285	+	32.1285i	1.04736	+	1.04736i	0.998821	+	0.0485386i	$0.0154564\pi$
$941$	32.1285	+	32.1285i	1.04736	+	1.04736i	0.0485386	+	0.998821i	$0.484544\pi$
$942$	−4.03376	+	24.6077i	−0.131427	+	0.801762i
$943$		−	21.4914i		−	0.699856i
$944$	4.53843	−	8.86026i	0.147713	−	0.288377i
$945$	−19.2101	−	6.55309i	−0.624904	−	0.213172i
$946$	5.82613	+	11.4496i	0.189424	+	0.372257i
$947$	−31.1625	+	31.1625i	−1.01265	+	1.01265i	−0.0127273	+	0.999919i	$0.504051\pi$
$947$	−31.1625	+	31.1625i	−1.01265	+	1.01265i	−0.999919	+	0.0127273i	$0.995949\pi$
$948$	5.99858	−	11.6022i	0.194825	−	0.376821i
$949$	−1.15889	−	1.15889i	−0.0376191	−	0.0376191i
$950$	−12.7392	−	4.14675i	−0.413314	−	0.134538i
$951$	27.9922	−	38.1365i	0.907708	−	1.23666i
$952$	3.17726	−	19.8542i	0.102976	−	0.643479i
$953$	23.9408			0.775520			0.387760	−	0.921760i	$-0.373249\pi$
$953$	23.9408			0.775520			0.387760	+	0.921760i	$0.373249\pi$
$954$	−37.5081	−	0.384896i	−1.21437	−	0.0124615i
$955$	−7.61160	+	7.61160i	−0.246306	+	0.246306i
$956$	−24.0428	+	33.0177i	−0.777599	+	1.06787i
$957$	3.76857	−	0.578110i	0.121821	−	0.0186876i
$958$	−18.5459	−	36.4466i	−0.599191	−	1.17754i
$959$	−14.1272			−0.456190
$960$	31.4597	+	44.0438i	1.01536	+	1.42151i
$961$	24.6520			0.795227
$962$	−4.79184	−	9.41696i	−0.154495	−	0.303615i
$963$	29.0682	+	15.1689i	0.936711	+	0.488812i
$964$	10.7435	−	14.7540i	0.346026	−	0.475194i
$965$	35.1091	−	35.1091i	1.13020	−	1.13020i
$966$	5.69159	+	7.92340i	0.183124	+	0.254931i
$967$	−35.6844			−1.14753			−0.573767	−	0.819019i	$-0.694519\pi$
$967$	−35.6844			−1.14753			−0.573767	+	0.819019i	$0.694519\pi$
$968$	8.88885	−	55.5450i	0.285699	−	1.78529i
$969$	−9.16644	−	6.72816i	−0.294468	−	0.216140i
$970$	−58.0050	−	18.8813i	−1.86243	−	0.606241i
$971$	33.2472	+	33.2472i	1.06695	+	1.06695i	0.997592	+	0.0693607i	$0.0220959\pi$
$971$	33.2472	+	33.2472i	1.06695	+	1.06695i	0.0693607	+	0.997592i	$0.477904\pi$
$972$	30.9070	−	4.09395i	0.991341	−	0.131313i
$973$	−11.6721	+	11.6721i	−0.374189	+	0.374189i
$974$	3.52524	+	6.92783i	0.112956	+	0.221982i
$975$	18.8641	−	25.7004i	0.604135	−	0.823072i
$976$	10.2074	+	5.22844i	0.326729	+	0.167358i
$977$			51.7092i			1.65432i	0.561963	+	0.827162i	$0.310046\pi$
$977$			51.7092i			1.65432i	−0.561963	+	0.827162i	$0.689954\pi$
$978$	−8.45138	−	1.38537i	−0.270245	−	0.0442993i
$979$	8.27391	+	8.27391i	0.264435	+	0.264435i
$980$	−1.21386	−	7.71746i	−0.0387755	−	0.246525i
$981$	23.1113	−	44.2882i	0.737886	−	1.41401i
$982$	−15.8272	+	48.6225i	−0.505065	+	1.55161i
$983$			11.7952i			0.376209i	0.982149	+	0.188105i	$0.0602344\pi$
$983$			11.7952i			0.376209i	−0.982149	+	0.188105i	$0.939766\pi$
$984$	0.170977	−	26.4348i	0.00545054	−	0.842712i
$985$		−	68.9296i		−	2.19628i
$986$	3.78631	+	1.23249i	0.120581	+	0.0392504i
$987$	−1.31342	−	8.56191i	−0.0418067	−	0.272529i
$988$	−1.95078	+	2.67898i	−0.0620625	+	0.0852298i
$989$	−4.60309	−	4.60309i	−0.146370	−	0.146370i
$990$	−64.4562	−	65.7928i	−2.04855	−	2.09103i
$991$			4.96971i			0.157868i	0.996880	+	0.0789341i	$0.0251517\pi$
$991$			4.96971i			0.157868i	−0.996880	+	0.0789341i	$0.974848\pi$
$992$	10.0511	+	10.1050i	0.319122	+	0.320833i
$993$	−42.7895	−	31.4074i	−1.35788	−	0.996685i
$994$	−7.24437	+	3.68631i	−0.229778	+	0.116923i
$995$	−44.8768	+	44.8768i	−1.42269	+	1.42269i
$996$	−42.5502	+	13.5468i	−1.34825	+	0.429248i
$997$	−37.4527	−	37.4527i	−1.18614	−	1.18614i	−0.978126	−	0.208015i	$-0.933300\pi$
$997$	−37.4527	−	37.4527i	−1.18614	−	1.18614i	−0.208015	−	0.978126i	$-0.566700\pi$
$998$	−1.53242	+	4.70773i	−0.0485078	+	0.149021i
$999$	−6.98549	+	20.4777i	−0.221011	+	0.647884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.d.155.15	yes	48
3.2	odd	2	inner	336.2.s.d.155.10	✓	48
4.3	odd	2		1344.2.s.d.911.14		48
12.11	even	2		1344.2.s.d.911.24		48
16.3	odd	4	inner	336.2.s.d.323.10	yes	48
16.13	even	4		1344.2.s.d.239.24		48
48.29	odd	4		1344.2.s.d.239.14		48
48.35	even	4	inner	336.2.s.d.323.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.10	✓	48	3.2	odd	2	inner
336.2.s.d.155.15	yes	48	1.1	even	1	trivial
336.2.s.d.323.10	yes	48	16.3	odd	4	inner
336.2.s.d.323.15	yes	48	48.35	even	4	inner
1344.2.s.d.239.14		48	48.29	odd	4
1344.2.s.d.239.24		48	16.13	even	4
1344.2.s.d.911.14		48	4.3	odd	2
1344.2.s.d.911.24		48	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.641365 + 1.26042i) q^{2} +(-0.262630 - 1.71202i) q^{3} +(-1.17730 + 1.61678i) q^{4} +(-2.76208 + 2.76208i) q^{5} +(1.98942 - 1.42906i) q^{6} +1.00000 q^{7} +(-2.79289 - 0.446945i) q^{8} +(-2.86205 + 0.899256i) q^{9} +O(q^{10})\)	\(q+(0.641365 + 1.26042i) q^{2} +(-0.262630 - 1.71202i) q^{3} +(-1.17730 + 1.61678i) q^{4} +(-2.76208 + 2.76208i) q^{5} +(1.98942 - 1.42906i) q^{6} +1.00000 q^{7} +(-2.79289 - 0.446945i) q^{8} +(-2.86205 + 0.899256i) q^{9} +(-5.25287 - 1.70987i) q^{10} +(-3.92989 - 3.92989i) q^{11} +(3.07715 + 1.59095i) q^{12} +(-1.26876 + 1.26876i) q^{13} +(0.641365 + 1.26042i) q^{14} +(5.45415 + 4.00334i) q^{15} +(-1.22793 - 3.80686i) q^{16} +7.10884i q^{17} +(-2.96906 - 3.03063i) q^{18} +(-0.652997 - 0.652997i) q^{19} +(-1.21386 - 7.71746i) q^{20} +(-0.262630 - 1.71202i) q^{21} +(2.43280 - 7.47379i) q^{22} +3.98276i q^{23} +(-0.0316852 + 4.89888i) q^{24} -10.2582i q^{25} +(-2.41291 - 0.785428i) q^{26} +(2.29121 + 4.66373i) q^{27} +(-1.17730 + 1.61678i) q^{28} +(-0.280064 - 0.280064i) q^{29} +(-1.54778 + 9.44211i) q^{30} +2.51952i q^{31} +(4.01068 - 3.98929i) q^{32} +(-5.69595 + 7.76016i) q^{33} +(-8.96010 + 4.55937i) q^{34} +(-2.76208 + 2.76208i) q^{35} +(1.91560 - 5.68599i) q^{36} +(2.94433 + 2.94433i) q^{37} +(0.404238 - 1.24186i) q^{38} +(2.50536 + 1.83893i) q^{39} +(8.94869 - 6.47969i) q^{40} -5.39610 q^{41} +(1.98942 - 1.42906i) q^{42} +(-1.15575 + 1.15575i) q^{43} +(10.9804 - 1.72709i) q^{44} +(5.42140 - 10.3890i) q^{45} +(-5.01994 + 2.55441i) q^{46} +5.00105 q^{47} +(-6.19495 + 3.10203i) q^{48} +1.00000 q^{49} +(12.9296 - 6.57924i) q^{50} +(12.1705 - 1.86699i) q^{51} +(-0.557588 - 3.54501i) q^{52} +(6.25168 - 6.25168i) q^{53} +(-4.40874 + 5.87903i) q^{54} +21.7093 q^{55} +(-2.79289 - 0.446945i) q^{56} +(-0.946449 + 1.28944i) q^{57} +(0.173374 - 0.532620i) q^{58} +(1.75981 + 1.75981i) q^{59} +(-12.8937 + 4.10500i) q^{60} +(-2.02736 + 2.02736i) q^{61} +(-3.17564 + 1.61593i) q^{62} +(-2.86205 + 0.899256i) q^{63} +(7.60048 + 2.49654i) q^{64} -7.00883i q^{65} +(-13.4342 - 2.20218i) q^{66} +(-0.986955 - 0.986955i) q^{67} +(-11.4934 - 8.36924i) q^{68} +(6.81859 - 1.04599i) q^{69} +(-5.25287 - 1.70987i) q^{70} +5.74760i q^{71} +(8.39532 - 1.23234i) q^{72} +0.913402i q^{73} +(-1.82269 + 5.59948i) q^{74} +(-17.5622 + 2.69410i) q^{75} +(1.82452 - 0.286976i) q^{76} +(-3.92989 - 3.92989i) q^{77} +(-0.710970 + 4.33723i) q^{78} -3.77043i q^{79} +(13.9065 + 7.12323i) q^{80} +(7.38268 - 5.14744i) q^{81} +(-3.46087 - 6.80133i) q^{82} +(-9.11508 + 9.11508i) q^{83} +(3.07715 + 1.59095i) q^{84} +(-19.6352 - 19.6352i) q^{85} +(-2.19799 - 0.715470i) q^{86} +(-0.405923 + 0.553029i) q^{87} +(9.21930 + 12.7322i) q^{88} -2.10538 q^{89} +(16.5716 + 0.170053i) q^{90} +(-1.26876 + 1.26876i) q^{91} +(-6.43923 - 4.68891i) q^{92} +(4.31347 - 0.661699i) q^{93} +(3.20750 + 6.30340i) q^{94} +3.60726 q^{95} +(-7.88308 - 5.81868i) q^{96} +11.0425 q^{97} +(0.641365 + 1.26042i) q^{98} +(14.7815 + 7.71356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) 48 * q + 6 * q^6 + 48 * q^7	\( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more